Can a woman get pregnant after her husband gets a vasectomy?

Possibly: There is a period of time when viable sperm is still stored in his reproductive track after vasectomy. Also vasectomy failures can occasionally occur.

Low risk, but yes: Every form of birth control, even tubal ligation and vasectomy, has a failure rate. The chinese studies of the no scalpel technique, now performed widely, had a 0.2% pregnancy rate based on over 100, 000 procedures performed. That's a huge group of patients, a very small rate of pregnancy but it can still happen. Tubal ligation has a similarly low rate of inintended pregnancy.

In vitro: Will need to extract sperm from testicle and have artifciial insemmination by a fertility specialist or can have a vasectomy reversal.