This could be an episode of the animated series "Aeon Flux", in particular episode S03E03 "Thanatophobia".
The synopsis from Wikipedia says:
[...] two Breen lovers, Onan and Sybil, seek to escape from Bregna into Monica through a gap in the frontier. The escape is almost a success, but one of the turrets shoots Sybil in the back, destroying one of her vertebrae. Now she can only stand up straight when a special ampoule is inserted, though when she takes it out she has otherwise impossible flexibility, making crossing successfully a stronger possibility.
At the end, as you remembered, the escape plan fails.
The series style and themes are peculiar, and they could be described as cyberpunk; it aired on MTV in the Nineties, which matches too.
The only element that doesn't match is that it's a series, not a movie.