If your mother's stay is in a skilled nursing or rehabilitation facility while recovering from her injury, she might continue to qualify for Medicare's nursing facility benefits. This depends on whether Medicare considers that she is improving while in the facility, rather than merely being cared for because she needs assistance. If Medicare continues to pay after her first 20 days (during any one benefit period) of nursing facility coverage has been used up, Medicare pays all covered charges for up to 100 days except a daily "coinsurance amount" of $133.50 per day, for which your mother would be personally responsible. If she has a private Medigap supplemental insurance policy, that policy might pay some or all of this coinsurance amount. After 100 days of skilled nursing facility coverage in any one benefit period, Medicare no longer pays any of the cost.
If Medicare will not continue to cover your mother's stay in the facility, or if she cannot afford the Medicare coinsurance amount, she might qualify for Medicaid coverage of her stay. If her only assets other than her home (Medicaid won't count the home in determining her eligibility) are the $2,000 in the bank, it sounds like she is likely to qualify. It also depends, however, on how much her monthly income is from Social Security, pensions and any other source -- it has to be quite low for her to qualify for Medicaid. The exact amounts depend on the state she lives in. If she qualifies for Medicaid coverage of her nursing facility stay, Medicaid can pay the full amount for an unlimited time (as long as her doctors certify that she needs nursing facility care).
To find out what the Medicaid rules are in the state where your mother lives, and to learn where and how you can help her apply, go online to any search engine and enter the word Medicaid and the name of the state. Or, you can call the Eldercare Locator toll-free at 800-677-1116 and ask them for contact information for Medicaid in your father's state. You can also discuss Medicaid eligibility with the ombudsman or administrator at the nursing facility where your mother is staying.