How go I have a person name removed from a homeowner deed?

While the other person on the deed could gift you his interest and record a deed to this effect, if he (and you) are doing so in an attempt to evade current creditors, this would be fraud.  Note that although an assisted living facility does not provide medical care, there is still a bill for room, board and non-medical assistance which must be paid.  If your husband dies in the assisted living facility (or in a nursing home), suit could be brought against his estate.  In some states there are deeds which pass title on death, avoiding probate.  You might want to discuss this possibility with an elder lawyer.  You can find one near you using the Find a Lawyer function on the website of the National Academy of Elder Law Attorneys (www.naela.org).