I can't help with his fate but you apparently listed the wrong birth month? I believe the attached 1 October 1849 birth is him (last entry).
Here is the family in 1850, but they may have moved as I don't find Mads' confirmation in Ballum records.
Tønder, Tønder, Højer og Lø, Ballum, Østerende, , en Gaard, 70, FT-1850
Name: Age: Marital status: Occupation in household: Occupation: Birth place:
Peter Hansen Møller 25 Gift Indsidder, Dagleier, Huusfader Her i Sognet
Mette Kirstine Beyer 25 Gift hans Kone, Syer Slesvig
Mads Hansen Møller 1 Ugift deres Søn Her i Sognet
Caroline Simonsen 29 Ugift lærer Syning af Huusmoderen Hoe Sogn, Ribe Amt
Christine Petersen 23 Ugift lærer Syning af Huusmoderen Aal Sogn, Ribe Amt