You can create new users in the other domain. Those users are going to have different SIDs, different userPrincipalNames, different distinguishedNames, etc. The groups in which they are members won't have them as members in the new domain so forget about maintaining the memberOf property value of the users.
Because the two domains can't communicate with each other the different SIDs won't matter (and there's always the old sidHistory property to help if there is communications -- but whether that'll work without a trust I can't say). Group membership will be a problem, especially if you have nested groups.
If you do create new users (not difficult) you can count on things not working properly for a while. And count on possibly creating new groups and adding those new users to them).