What is the amount of money that you can legally set aside or remove from an account before your loved one is moved into a nursing home?

There isn't any maximum amount.  Transferring those funds to another account  to pay for a funeral is advisable.  Due to the high cost of a nursing home, it would be advisable to file an application for your Great Grandmother with Medicaid to help pay for the nursing home.  Medicaid has limits on income and assets that one can have in order to be eligible.  You can transfer or otherwise dispose of assets/income so that your Great Grandmother could become eligible for Medicaid.  If your Great Grandmother's income from Social Security and/or other sources exceeds a certain amount determined by Medicaid, then she may be liable for a patient's share of the nursing home cost.  The social worker at the nursing home may be able to help you apply for Medicaid for your Great Grandmother.