Can a nursing home take $52 personal allowance from resident?

My 54 year old sister has been in a nursing home for about three years. She is on Medicaid and SSD. The nursing home takes her SSD and gives her $52 per month for personal expenses. At the time of my sisters illness that put her in the nursing home she had student loans. Since she only has the $52 per month, she is not able to pay them and the government is garnishing her SSD. The nursing home is now saying that she must give the $52 back to the nursing home since they are not getting her full SSD check due to the garnishments. Are they correct, can they take her personal allowance? This would leave her penniless (she has no assets) and this just sounds very unfair if true.
Thank you.