Do not try this; I am sure there are better ways out there for most tape problems. I am posting this as it may help with further understanding of underlying issues and precautions.
I have a bubble on the start of a prerecorded tape (I got it for free on top, so no problem here), it lead to dropouts and switching to side B. Playing with a wet felt pad made it a little better, but still dropouts.
I cleaned it with isopropanol on a cotton swab while on top of the felt pad, it left it bent downwards a little. I played it like this, the first times utterly horribly squealing at that spot (stick slip), but after many winding/re-winding attempts, it works so nicely that I can barely see some flickering of the error correction while in service mode.
I also learned that one reason for the gap between the first actual tape segment from the leader and the audio is that if it is damaged somehow, it still can read the fast forward command in the worst case a second later, and it does not matter that much.
What is the worst thing you have done to a tape or a player that solved a problem?