There is a link from the button mechanism down to the latch that has plastic clips on either end. When the plastic clip and the hole wear a bit, the clip pops out of its hole and the link just dangles.
On e36 cars with fold down rear seats, this is no problem. You just crawl in the trunk and snap up the trunk lid liner and reach in and pop the trunk. Then replace the plastic clips on the ends of the link. My daughter did this on her '97 last year.
In your case, you will likely have to find a round rubber sheet metal plug at least a half inch in diameter. Then remove your license plate and drill a hole that fits your plug near the center of the license plate. Then reach in with a hook and release the trunk lid. Then repair. I have not done this, but it is the only solution I can think of.
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Your Ride: 1995 325i Convertible
Put away the drill
God no...don't drill a thing. On a convertible, remove the back seat and then the screws that hold that ski holder thing (useless) that is normally covered by the middle arm rest. get yourself a good flashlight and something long and steady. When mine did this, i had to reach in with arms and tools to get to the latch, which then can be popped (provided you have 'unlocked" with key....by hitting the side of the latch upward.
It is tricky and hard to get at if you are any kind of sizeable person. I ended up using a golf iron to get the extension to the part once i got down and understood the mechanism. You catch that "connecting rod" and pop it. Look at the realoem diagram of the parts and note the connecting rod. If you can get your arms in and use channellocks or pliers then great....but if not, then use a long stick of wood or metal (hence the club) and pop it that way. Then use the tips above to replace the plastic nut connectors. Rarely is the lock smoked...it is almost always the failure of those plastic parts.
1995 325i Convertible
"Remember men, we're fighting for this woman's honour; which is probably more than she ever did. "