Limit switch doesn’t function on oil furnace

Yes. A bad high limit switch would cause this. The furnace is trying to purge the heat that it thinks is there. Normally the limit switch will reset when the temperature drops. A bad switch will remain open, so the blower will run continuously.

This is typically caused by poor air flow through the furnace, which is most often due to infrequent filter changes. The furnace continually overheats, and eventually the high limit does not reset.

Make sure to change the filter often, and insure that all registers and returns are open and free of obstructions.

You have a bad high limit switch, or the furnace is overheated. The high limit switch is in place to make sure the furnace doesn't heat up to the point that it damages itself, or anything around it. If the furnace gets too hot, the limit switch opens. When the switch opens the burners turn off, but the blower continues to run in an attempt to clear the heat. Once the heat is removed, the limit switch should reset (if it's an automatic reset type). In the case of a bad switch, it never resets, so the burners never come on.

Limit switches can go bad with age, but more often than not fail due to overuse. Dirty filters, blocked return ducts, closed registers, really anything that restricts air flow through the system can cause the furnace to overheat. If this happens too often, the limit switch will die prematurely.

Have a local licensed HVAC technician install a new limit switch.