I am not an attorney, but all of the lenders that I have worked for or worked with on a loan, have required that any delinquent taxes are paid prior to the lender funding the loan. This would apply to a purchase or refinance.
From a lender’s viewpoint, they require that all liens be cleared from title before their transaction, because they want to be in 1st position to get their money back if there is a loan default down the line.
In addition to clearing any items that will affect the property title, many lenders will also require that the property taxes be impounded in an escrow account to help make sure that they are kept current on the new loan.
Great Question. During a refinance the lender will request a preliminary title report which will show all outstanding liens against the property, including tax liens. The lender will require property taxes to be paid current, however the delinquent taxes may be paid from the proceeds of the loan. So, to answer your question, the taxes are paid off from the proceeds of the loan and do not transfer to the new lender. If the title company did not include the delinquent taxes on the preliminary title report, then it it is possible that the new lender would fund the loan without paying off the lien, however that is an unlikely scenario.