Wow! Big thanks for all your replies and ideas.
Now to clarify, summarise and ask further questions:
Nouveau Riche - the term tends to be associated with those that have made (some degree of) money and constantly flaunt it, as if it makes them better than everyone else. This is what the people are like, rather than those who've successfully swelled the coffers and remain grounded about it. They expect people to bow and scrape to them because they perceive themselves to be better than those around them. Definitely "Keeping Up Appearances" types (a UK TV reference for non-UK people). Locals are decent, but fed up of the attitude!
You'll need to be careful how you portray it so it clear it's that and not snobbery. Maybe balance it out by showing they're not snobs, e.g. maybe another family on the street are wealthy working class (and it's obvious, e.g. by their accents etc) but they're not obnoxious and they're accepted. And maybe someone in the street does fundraising for Shelter or other homeless charities or they all collect things for the local food bank.
No homeowner association - people are relatively house proud so maintain their properties.
People might notice:
* Getting rid of the gardener
* Child(ren) being moved from a fee-paying school to free state education
* Downsizing the car(s)
* Debt - although I assume they'd do everything possible to cover this up
* Not maintaining the house, or only doing what work people will see
Tactics:
* Excluding them socially
* Gossip - even if it is based on observation/experience
* Potential sabotage of property (e.g. car) or garden
Questions:
1. Could they pretend to flaunt their dwindling wealth more as things decline behind closed doors? For example, upgrading the car rather than downgrading? Maybe they'd "borrow" money from the business/overdraft?
Up to a point they could. Their credit rating would get worse and worse and they'd end up being unable to take out any more loans.
If they start off with a good credit rating, they can probably borrow a lot before their credit rating goes bad (i.e. when they start to fail to make repayments on time). They probably would be able to get credit cards with a load of different banks and if they did that when they had lots of money they always paid them off on time and in full, their spending limits on each card would be very high - I've heard of people having credit limits in tens of thousands because they have excellent credit ratings and always pay everything off in full each month. I don't know how long it would take to get a credit limit that high though. It probably takes years.
At the point they start struggling financially, they could max out all their credit cards and get a crap ton of expensive goods. It wouldn't last long though because they'd have to at least make minimal repayments on each card and if they're all maxed out to a very high level, the repayments will be much higher than the money they've got coming in and they'd probably end up having to declare themselves bankrupt and they'd be repossessed/evicted when they stop paying the rent/mortgage.
They wouldn't immediately be declared bankrupt, they'd start off by making agreements with each of the banks they owe money to - they have departments you can call when you get into difficulty and they can make agreements for lower payments, less interest, etc to help people pay back what they owe but their credit card would be frozen and their credit rating at that point would be shit so they won't be able to borry any more money from anyone.
There are companies that do debt consolidation loans, they may go for something like this to avoid declaring bankruptcy - the company lends money to pay off all the debt, but they then owe this company instead, but they will do smaller monthly repayments with a much longer term. The term might end up being longer than their mortgage term and it's a bit like having a second mortgage, but without owning a house at the end of it.
While they still have a good credit rating, they could get a better car on credit. Say the first car was bought in cash without any credit plan because they had loads of money. If they sell that car that will give them money they can use for whatever. Then they get a new car on payment plan with the garage, which could be a better model than their original car (the garage is likely to encourage them to upgrade the car and get the new one on credit, because they make more money that way). I don't know how much deposit they'd have to pay initially, but they have the money from selling the first car so they'd be able to pay it. If you go to any car dealership online you can see how much they'd have to pay in deposit and monthly repayments to own any make/model of car. Of course, if they're doing the above with their credit cards then buying a car this way is worse than foolish and would hasten them on the road to bankruptcy, but it could be done while their credit rating is still good. The garage would credit check them before agreeing to the plan and as long as that came out fine, they'd make the agreement.
Borrowing from the business - if a self employed person's in financial difficulty, then would the business even have funds that they could use? If they're a sole trader or 100% shareholder in his own business then they'd be earning the proceeds of the business anyway. If it's the case that the business is doing okay but they're living beyond their means, there wouldn't be additional funds. If they're not a 100% shareholder of their company and they're using additional business funds for their own use, this would be technically possible but would create an epic level legal shitstorm if they're doing this without the knowledge/permission of the other directors/shareholders, because that's basically taking their share of the business/funds. I don't know the legal technicalities here you'd have to look it up, but if you want the character(s) to face an epic level legal shitstorm as well as going bankrupt, then they can do this. I mean it would certainly add spice to the story.
Also bear in mind that if they were never as rich as they were claiming to be, they wouldn't get a good enough credit rating to borrow huge amounts of money. If they're maxing out credit cards from the start then they're never going to get that good a credit rating. The amount they can borrow and the amount of financial armageddon they find themselves in would be limited - which is the whole reason why there's a credit rating system to begin with.
2. Say the neighbours decide covertly nasty/subtle illegal is the way to go, what could they do that wouldn't get them caught?
I don't think they'd need to do anything if they're making the financial decisions stated above. They'd be bankrupt and repossessed/evicted within a few months. Now it could be that one of the neighbours is a financial advisor who deliberately gives bad advice to them with the intent that they'd end up bankrupt, repossessed/evicted and out of the neighbourhood. That would risk their professional reputation though, as this family may go round telling everyone what a crap financial advisor they are. There might be some other more subtle ways they could nudge the family in the direction of an epic financial meltdown.
Bear in mind that the data protection act governs what companies (including all employees of companies) can and can't do with people's personal information, so it would be illegal for someone to look up their neighbours on the system at work and then tell other neighbours what they found out about them or use the information to do something bad to them (or even use the information in any way outside of work for that matter).