When you make a top like that you use liquid silicone to bond the already cast silicone to the fabric- essentially using it like glue. It soaks in the fabric and bonds to the cast silicone as well- it reaaaaallly bonds it on there. If you wanted to put it on a new bra you'd have to cut the old bra to pieces. You'd have to have the top layer of fabric from the original bra intact probably, since it's bonded with the silicone. But with careful cutting and ripping away any padding inside, you could probably do it. You could probably put it on a new bra after that with some glue and clamping. But it would be messy and may end up damaging your bra, maybe even making it useless depending on how the deconstruction goes and if there's slip ups. It's up to you!

You could always pull out the underwire, and cut off the bands on the bra and sew netting onto it to use for straps instead