No. Crumbling foam is the most common vintage speaker failure there is, and it is also one of the most fixable. The foam surround has a service life, and when it goes the driver underneath is usually fine.
You have two honest paths:
Refoam it. Replacement surrounds are sold as kits, and good sellers make the fit decision objective rather than guessy: kits are specified by four published measurements (surround outer diameter, roll ends, cone outer diameter, and surround inner diameter). Measure yours, match the numbers, and the kit either fits or does not. The glue work is patient rather than skilled: center the cone, glue the inner edge first, let it set, then do the outer lip.
Replace the driver. If the cone itself is damaged, copy woofers are made and sold by the original part number for a lot of common brands (Polk, Boston, Paradigm among them), so you are not stuck with "close enough" from a general parts bin.
Two traps worth knowing before you order anything:
- Not every woofer glues the same way. Advent's Masonite woofers take the surround on the back of the Masonite ring and the front of the cone, with the roll inverted (belly in). Metal-basket woofers are the opposite. And whatever you do, do not pop the Masonite ring off; it is brittle and it does not forgive.
- Some "foam" is actually rubber. Polk's Monitor series used rubber surrounds from the factory, and the correct kit for those is rubber, not foam. Check what your speakers actually came with before ordering.
If you are not sure which family yours is, post the brand, the model, and a photo of the woofer. Somebody here has refoamed that exact driver and can tell you where the glue goes.