visit visa switching to assylum

Hi

My family are here on visit visa. they made a silly mistake and went to the embassy in croyden and filed for assylum. they have been called in for interview and the embassy will be offering them 3 days accomodation. During the 1st interview my elderly aunt who was questioned some of answers were incorectly answered whilst in interview stage we think they have got suspicious that they are here illegly which they are not, they have been issued with i.d cards due to this

The family are worried, thinking they will be deported back, the visiting visa expires in month, they are contemplating if they should go back to pakistan or stay and continue with assylum. does this have any implications to there records.

If they apply for assylum .