Of course it is possible to design a dual-purpose (SHA256 cracking/mining) chip, it would very likely mean larger die size and more layers thus higher NRE costs and higher end-product costs.

End result being customers paying more to get the same hashrate. There isn't that much demand for SHA256 cracking actually, in fact sha256 is not widely used, thus it is highly unlikely you'd ever pay off your ASIC miner in case bitcoin collapses simply because demand is low. A better idea would be to create a dual-use chip that can perform custom number of PBKDF2 iterations, it can then be easily reused by software to crack different stuff (WPA-PSK, ZIP 3.x, protected OpenOffice docs, FileVault, encrypted IOS/blackberry backups, etc). Problem being PBKDF2-SHA1 is so radically different as compared to SHA256 that you'd be much better off selling two different boards together.

Overall though fast ASICs are not quite useful for hash cracking unless you are a three-letter agency that can afford producing lots of different designs. Also unlike bitcoin mining, it is not all about speed, cleverly exploiting low password entropy by reducing keyspace in some way, generally works better (otherwise cracking passwords of length >=10  would be extremely uncommon). Simple bruteforce attacks are dumb and generally it's much more practical to write some good wordlist mangling rules as compared to bruteforcing. Even statistical attacks like ones based on markov models are generally much better than bruteforcing. Yet markov attacks require good input models and rule mangling requires much more skill as compared to bitcoin mining.