'Enemy Mine' was based on a book by the same name, which itself was based on an older movie called 'Hell in the Pacific' (staring Lee Marvin and Toshirō Mifune; two excellent actors for that style of movie.) The original movie did have an alternate ending that was changed due to being too abrupt. (And too much of a downer.)
Stealing from the IMDB Alternate Version notes:
American version featured an alternative ending where the two get drunk and walk off in separate directions arguing at each other; in the British version they start yelling and a bomb from the sky falls and blows everything apart.
To increase the viewer's sympathy with the characters,:
Enemy mine uses the Zammis sub-plot; he, in effect, replaces his parent, and is used as a foil to show Davidge's development as a character. The ending also takes things farther, with them becoming (in-effect) family. Basically kicking the emotional impact up a few notches.
I'd take a guess that an updated variant on the British version is what you are talking about.
A simple version would have ended with a subsequent bombing taking them all out after they have become friends/family. This style of ending was popular for a while in the 60s and 70s, although it was basically just a rather heavy-handed way of underscoring the horrors of war. (You've have seen two characters grow and develop, finding a common ground and showing that peace has a chance... and it ends up being pointless, as they both die. War sucks.)
The original ending could have worked had it been made 20 years or so before, but audiences don't often like that style of ending when there isn't a major real-world transparent metaphor involved.
Dunno how the 'mine' aspect fits in; I suspect it may be apocryphal and/or someone screwing with people. I suppose the scavenger's processing ship evokes images of a mine, but I can't imagine anyone would thing that would do anything except confuse the viewer, if they tried to associate it with the title.
I had a silly idea.. and e-mailed the author via his website. Here's his response (cleaned the formatting up, slightly to make it readable here)-- make of it what you will:
Sent: Sunday, June 18, 2017 7:49 PM
To: Barry Longyear
Subject: Enemy Mine
A question was asked, some time ago, on the SciFi Stack Exchange site where
the following statement was given to back up the answer:
"Author Barry Longyear reported at a convention that the studio insisted on
adding a subplot involving a mine, thinking the audience would not realize
that the "Mine" in the title was a possessive (as in "My Enemy") rather than
an object. "
I'm just curious if this is true, or this is simply an apocryphal story, as
so many 'said at a con' stories are.
Thank you for your time :)
-[my email redacted]
From: Barry B. Longyear
Sent: Tuesday, June 20, 2017 4:49 PM
To: [my email redacted]
Subject: RE: Enemy Mine
It was a guess, and since the script writer borrowed the slave-mine from
Robinson Crusoe on Mars and stuck it in the movie, probably an accurate