@Fr If an off-line payment failed when Square reconnected to the Internet there is nothing that square can do to get that money, that card was declined. Just like if the person's card was declined while they were standing in front of you, you would need to ask for a different card.  You need to contact the buyer and arrange another form of payment. 

I don't use offline mode but if I did I’d make sure to collect the name, phone number, and email address so that I’d have a way of contact.