Depending on the type of loan on the home ..
If the loan is currently an FHA loan ... you can Assume the loan thru the current lender . Allowing you to keep the same interest rate and payment. You will have to qualify for the loan..but it is a lot cheaper than a refinance. (and no appraisal needed)
VA loans are assumable too.. but the assumption of a VA loan by a non vet will tie up some of the Vets entitlement for their next loan (basically how much they can borrow on another home)
Conventional loan.. ARM (Adjustable Rate Mortgage) are assumable.
Conventional loan .. Fixed rate is not assumable..your sibling can refi the loan with proof that they have paid the mortgage by themselves for at least 1yr (cancelled cks or bank statement payments (has to be clear the payment went directly to the lender not you).
I hope this helps