Yes, they will need to establish the purpose of their trip to the U.S., and if they have already stayed a long time and have no firm date when they plan to depart, they should expect trouble.
The above is intended only as general information, and does not constitute legal advice. You must speak with an attorney to discuss your individual case.
Their applications will be deemed abandoned once they leave the US.
Mr. Shusterman is a former INS Trial Attorney (1976-82) with over 35 years of immigration experience. His response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.