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Hi I'm Brian and I'm here to help!
Just to be sure it is actually your fan relay that's the issue (and it usually is on that model), you should remove the wire connected at terminal G on the air handler's low voltage terminal strip and turn the power back on. If the fan still continues to run then it is indeed your fan relay. It's most likely the small timer relay circuit board attached to your fan relay (if equipped). This was a very common failure on that model.
The Trane TWE air handler has had a VERY long model run! There were several different relays used throughout the years. If you can get a part number off the relay or your Service Facts sheet in the air handler, I can source the replacement or substitution for it.
If it is the little circuit board attached to the fan relay that failed and you don't care about the off cycle delay (fan runs for 90 seconds or so before it shuts off after the call has been removed), If you take a close up picture of your relay showing the wiring to it, I can help you remove the circuit board and bypass it. Chances are good the relay is still fine. Upload the pic here by using either the paperclip icon in the text formatting toolbar at the top of your reply dialog box where you type your replies to me, or if you don't have the paperclip, the 'Attach Files' button in the lower left of the same dialog box. Then you just browse to the picture file on your computer.