I need to access my old work Dropbox account, but I'm asked for a one-time code that I can't access.

My old work would not grant me access, they were taken over by a company that is hard line and there's no way they'd grant me access.  It's been a little over 12 months but when I try to log in, it accepts my username and PW but tried to do the email verification and doesn't offer any other methods other than email.  If it did phone or something like that, would work fine.  Would hate to see what would happen if, for example, when my verizon.com emails all were canceled because Verizon stopped offering that service.  Then how would someone get in???  You would think they'd have some plan for circumstances like that.