Husband Family Permit what to do

My cousin is German national.She has 2 kids.She is living in UK for 2 years.Her husband is holding Indian nationality.He was living in Germany.but now he moved to UK.He came with family during their last visit to Germany and at Heathrow Airport they stamp visa on husband passport valid for 6 month.it was just a stamp not a visa sticker.

My cousin want to extend her husband stay.She is not working and claiming benefits.She has worked in past a year ago.can she apply for husband family permit even she is on benefits?

is husband allow to work as the stamp just shows expiry date only?

plz advice