No they won't go after the money on Boost nor will they cancel your Boost account. Their TOS would need to warn you about this. It's just a lot simpler to send the account to collections and ruin your credit score.
As for the e-mail it's probably just some automated system that sends it out. If you transfer your number out then Sprint.com looses all records and I'm betting it sends that message automatically after a while. I had to visit a Sprint store, couple weeks after I transfered, to pay my final bill last time I ported from them since Sprint.com didn't have any records of me anymore.