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Typically, the life tenant would pay the ordinary carrying-costs: taxes, insurance, ordinary repairs, etc.
However, if the life tenant refuses to pay these things, the remainderman (owner) will have to pay to keep the title to the property clear. If the life tenant refuses to do these things, the owner can file a lawsuit to try and cancel the life tenancy.
If the life tenant doesn't want to live on the property, he/she can issue a quitclaim deed to the owner and give up his/her right to the property.