Once someone is in a nursing home, his or her finances are likely not much of an issue anymore. Possessions, however, are.
Do an inventory of everything your parent takes to the facility, from clothing to hearing aids. Take photos of all valuables, and mark the valuables that you can -- you can engrave dentures and tag prosthetic devices.
Be observant when you come to visit. Is mom not wearing her wedding band? Where are dad's glasses? Note explanations like, "Someone took it to get it cleaned." Jewelry can be switched out with fakes, and expensive frames with a drugstore pair.
Report missing items to the facility and consider a police report, as well, if you suspect theft. In some cases, facilities can replace the items, or your homeowner's insurance might cover it.