I've heard that many manufacturers have what are effectively secret warranties--that if you push a bit on a problem that is widespread and expensive, but out of formal warranty, they sometimes meet you halfway on the costs. According to this account over at Corvette Forum, the widespread and very expensive ABS repairs on the Corvettes are in that category--especially if you can demonstrate strong GM brand loyalty.
That wouldn't be difficult. What GM vehicles have I owned? 1964 Chevrolet Malibu station wagon (bought new by my parents, gave it to me when I graduated high school). 1973 Chevrolet Caprice wagon (used). 1977 Chevrolet Nova (new). 1978 Camaro Z28 (new). 1979 Pontiac Grand Am (new). 1983 S10 Blazer (new). 1984 Cavalier (new). 1986 Celebrity Eurosport wagon (new). 200 Corvette (used). 2000 Impala LS (new). 2001 Malibu LS (new). 2005 Equinox (new). 2007 Trailblazer (used).
It's worth a try. Even if it knocked the costs down to several hundred dollars to get the ABS repaired, it would make it practical to get the Corvette fixed--which would make it a lot more sellable.
UPDATE: Apparently, there was a chance, but not for a car more than ten years old. Oh well, it was worth a try.