They can get a job at the regional level or majors, but it is much harder and they will have to explain this in every interview. Not a fun thing to do. With the over 11,000 applications on file at my current airline, they'll bypass someone with a DUI vs someone with a clean record every time. Why take the chance that this person will do it again? However, it's not saying that it can't be done.
Make this a learning experience for your offspring. I'd advise you to not financially cover everything for them and make sure that this is something that they own up to and learn from this mistake.
I currently have 2 college friends that are flying at the majors with DUI's on their record. One a conviction, the other not convicted. Another college friend is stuck at the regional level because they have a DUI conviction and no major wants to hire them with the amount of clean apps on file at the current time.
In regards to hiring, it's all about timing. When apps are down, airlines will hire to fill seats, but when there are a flood of apps like the current time, DUI's will get bypassed.
I'm not saying that it's a career killer, but make it a learning experience.