Okay, whoo, thank you so much guys!!! Can't believe it bypassed me that...investigating a crime is not abandoning it, haha. I'm thinking the best thing is some compromise - a rudimentary instigation points towards and implicates a particular person - not the actual killer but someone who has reason to be suspected - who is dead at this point. So a bit different, but creating a similar scenario in a hopefully more plausible way.
I still don't find that plausible.
Sometimes it's better to start with what you want to happen plot wise, and then get someone with a background in forensics to advise you of the details that would fit your plot.
So, from your reply, it seems that you want to have the wrong person accused of the crime while the real murderer gets away with it, but as the wrong person is dead, no-one goes to court over it.
IMO a plausible way to achieve this would be that they dig up the body, but as it's been in the ground for 30 years, there's only skeletal remains left. The police do a proper, thorough, forensic investigation, and manage to identify who the victim is but not how they died. They strongly suspect foul play but not enough evidence has survived to be able to confirm even that they were murdered, never mind who killed them. It remains a cold case and they run out of avenues for further investigation.
Meanwhile, as it's a small island and everyone knows everyone else, there's lots of rumours flying around. Lots of people remember when the victim went missing and any relevant circumstances (e.g. who they were hanging around with, etc). The rumour mill concludes that the dead person must've done it and the police don't pay attention to the rumours - they've already done all the investigating they can and know they can't prove it, plus this person's dead.
A body being in the ground for 30 years will result of a lot of evidence being lost. An inconclusive investigation done properly is a lot more plausible than the police not bothering to investigate fully (that's what I'd understand by a "rudimentary investigation") when it's probably a murder.
The police botching the forensics could be plausible, if this fits with how the police are in your setting. This would increase the likelihood that the investigation would prove inconclusive. If the body's been dug up while building works are going on, there could be damage to the remains. There's no reason to suspect that there would be human remains there, so there wouldn't be archaeologists around to advise how to prevent damage. (Though AFAIK in the Republic of Ireland they do have archaeologists on standby when doing any kind of excavation work for building - you'd probably want to check stuff like that for your setting). Damage to remains, moving the body (which the police might do if not properly trained in forensics, say if a low ranking officer is the first on the scene and doesn't know better*) could contaminate the evidence and some evidence will come from how the body is located, so that also would be lost. This happened to Otzi the ice man
https://en.wikipedia.org/wiki/Ötzi because lots of people were able to access where he was emerging from the ice before archaeologists were on the scene. This resulted in a loss of potential evidence.
*this is very shabby police work - officers being that badly trained would have to fit with the way the police force is run in your setting.
Anyway, it's very plausible that even a thorough forensic investigation of a body that's been buried for 30 years won't provide conclusive evidence. It's even plausible that they could fail to identify the victim at all if they weren't resident on the island or known to anyone there.