If the account hasn't been active for 6 months (which appears to be the case) Basecamp may be able to get the handle. Policy: https://support.twitter.com/articles/15362-inactive-account-...

The last I heard, it needed to be entirely dormant (meaning not a single log in) for 30 months in order to be eligible to transfer. Though they might have a trademark claim that would likely help.

No, it won't be a problem.. I'm sure they're already talking to Twitter about it. I heard something along the lines of accounts inactive for 6 months can be seized by Twitter.