Calling it an epiphyte is too vague for us to be sure what's happened. If you can give us a little more detail on what it looked like, if it ever bloomed, how long you had it, that will help.
I have epiphytic bromeliads and a couple of epiphytic cacti. There are also epiphytic aroids and epiphytic orchids. All four of those terms (broms, cacti, aroids, orchids) are also huge classifications and meaningless without more detail.
Once the broms bloom, that mama plant will gradually wither and die, producing decaying leaves to feed and support the pup plants that offset. Are you talking about a longish strap like leaf from a rosette of leaves that pulled out easily, then all the others did, too? If it's a bromeliad, that's how they roll. There is usually a baby or pup or offset at the base, though.