A used refrigerator can be a sound purchase, but only if you can read what it has been through. Before you agree to take one home, settle five things with the seller and with your own eyes.
First, the age. Find the model and serial plate, usually inside the fresh food section or on the back, and find the manufacture date code. Ask the seller for the install year if they know it. If they do not, treat any year you are given as a rough figure, and plan from that. The appliances ranked page on this site shows typical service life for the major appliance types and is a good place to set expectations for the age you find.
Second, the door seal. Pull the gasket from the top, bottom, and corners. It should spring back and cling to the cabinet when you close the door on a sheet of paper. A seal that tears, hardens, or leaves gaps lets cold air out and makes the unit work harder. Some gaskets can be replaced, so ask whether the gasket for that exact model is still available before you decide.
Third, the running condition. Plug the unit in at the spot where it will live, or ask for power at the seller's site, and listen. Wait for the compressor to start and run, and note the sound. Check the interior for a strong odor, cracks in the liner, and moisture on the floor of the unit. Ask whether it has been running continuously or was switched off for a time.
Fourth, the move. Ask how the unit was transported and stored. A refrigerator laid on its side during a move or a storage period usually needs time to settle before it is powered, and the manual states how long. A unit that was stored for a long stretch or moved on its back needs more care before its first start. Find the manual by model number, read the settling note, and follow it.
Fifth, the terms. Ask what the seller will do if the unit does not run when you get it home. Ask for the return terms in writing, including how long you have to test it, who pays for the move back, and whether any remaining manufacturer warranty transfers and in whose name. A warranty that does not transfer is worth knowing before you pay. A verbal promise is not the same as a written return term.
Before the unit leaves the seller, measure the space it will go in, including the door swing and the clearance at the back and sides. Confirm the outlet is on a circuit you can identify in the panel. Write down the model, the serial, the seller's name, and the terms. Then the file starts, and the planning date can be set from the age you found.