Can an individual in a Medicaid nursing home be transferred to a Medicare and Medicaid nursing home if a bed is available?

Yes. Talk to someone in the business office of the new facility -- they should be able to help you through the transition and advise you about what steps to take. The only out-of-pocket cost should be transportation from one facility to the other.

The nursing home is understaffed and he is being neglected. It is a local move.

It depends. Are you talking about moving from one nursing home to another in the same city or state? It can be done - with lots of attention to paperwork details and at YOUR expense (you said they have no resources). Medicare and Medicaid will not move a patient from facility to facility simply for convenience/closer to family. If you are talking about moving from one state to another, it's more complex. Medicaid doesn't cross state lines. You have to get the person re-qualified for Medicaid in the new state after moving them there. You have to physically move the person there at YOUR expense. And speaking as the daughter-in-law of a person with Parkinson's and dementia, every change of locale ratchets up the dementia. What is the reason you want to move them?