那要看他们的身份是不是和你联着

1. If the spouse and children are dependants of the visa holder - for example, hu*****and has F1, wife and children are F2 or other type of depentant visa, hu*****and got caught working illegally, and will be deported, the wife and kids cannot stay either, since their status are 'attached' to the hu*****and's visa.
2. If the spouse and/or children are on separate visa - for example, hu*****and has F1, wife has separate F1 as well, children are born in US so they are citizen, if hu*****and got caught working illegally, and will be deported, the wife and kids should not be impacted.

I'm not an expert, above are my opinions only. You could consult with a lawyer, they normally have a free first time consulting session.