What exactly would've happened to Lydia if Wickham wouldn't marry her?
Her family would have disowned her - she would Never Have Been Spoken Of Again.
The likelihood is that she would have found herself another "protector" in the regiment - probably more than one, but she would never have been able to mix in society unless she was fortunate enough to have got herself a colonel or something who could have married her off to a servant as a cover for his interest in her (even so - socially she would drop several notches and not be mixing with the set she was used to.)
It is unlikely that she would have married well - "gentlemen" didn't marry each other's cast-offs. She would most probably have been shared around the regiment and ultimately ended up a gin-sodden harlot and died of the pox.
The world was very cruel to "fallen" women - there was little or no chance of redemption.
Meanwhile, her bad behaviour would have reflected upon the whole family. The other girls would have found good marriages next to impossible (all that bad blood in the family - no mane wants a wife who could be cuckolding him behind his back, so he didn't know if he was bringing up his own children or someone else's). The only chance the other girls would have had of marrying at all would have been if they entire family had nothing to do with Lydia. NOTHING. EVER.
The Gardeners would also have washed their hands of her - he may have been in trade, but they were respectable, and they had children to consider, too. Sexual "badness" (in women) was considered to rub off on others very easily.