Usually transistor goes first, locking on the coil and melting it.

LTG : )

An open TIP102 will do nothing , the coil will not find a ground. A shorted TIP102 will supply a ground even when not commanded and will lock the coil on until the current either blows the fuse or melts the coil.

...and at some point the windings of the melted coil with short and burn the TIP102 which will eventually become an open unless a fuse prevents it ... You don't what to know how I know this

Edit: After thoughts ... you can get a pretty good burn from the plunger of a melted coil if you take this apart while its still smoking

Trust me when I say this ... some people shouldn't even try to replace these transistors.

You could end up with a board that looks like this:

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The person that removed this transistor broke FIVE circuit traces ... impressive for a 3 leg transistor. One of them was the ground leg for all 8 TIPs on the board, this crippled the entire board.

The transistor shorts collector to emitter and the coil locks on. If the fuse does not blow the tip102, PCB and the coil burn up. If not the fuse, eventually either the coil burns open or the transistor does.

Why the transistors go bad is bigger mystery question. Specially when there was no catastrophic specific fail mode like the EMF eating diode broke loose from the coil or when something else in the driver circuit kept the transistor turned on too long.