So, if the police did suspect foul play, what would they do exactly? Would they set up in the person's home? Do television coverage of it? It's a woman in her late 30s, a teacher. Her daughter is a psychic who has been on the trail of a killer.
Remember Chandra Levy case ...
Get a warrant or permission to inspect the house
Collect evidence at house (looking for bloodstains, forced entry, getting hair samples for DNA, fingerprints, impound car for later, check workplace
Haul off computers for forensic checks on emails, activity
Send out the usual "missing person, foul play suspected" bulletins and make database entries
Check the sightings trail ... ask neighbors, co-workers, etc. the last time they saw her and if she was with anyone
Set up a "money trail" ... go through her bills and see what credit cards she has, get a warrant or subpoena for last known activity, as CC companies to alert them if any further use ...
Subpoena bank records and put a watch on the bank accounts for further activity
If ATM or gas station activity, get the videos and look at them to see if she was alone or not
Check the relationships: is anyone out to get her, does anyone stand to profit from her death, could she just be visiting friends unexpectedly.
One case I am aware of, the disappearance of a 65 year old woman ended when she and her new husband (70-something) came back from their Hawaiian honeymoon. The grown, out of town kids had been kept in the dark about the relationship, and they decided to pay a surprise visit to Mummy and Mummy wasn't at home and wasn't answering the phone.