QB
DT
Safety
If we loose Romo
If we loose Wilcox or Church
If we loose Hayden or McClain
We're screwed.
Weeden yikes
Heath yikes
Bishop ?
Hoping some of this gets thresh out this summer
Yes, most teams are screwed if their starting QB is out. I'm hopeful that Vaughan can beat out Weeden and be OK if he had to play 1 game. If Romo was out long term they're screwed and there are very few backups on any team that even if they Cowboys had that player would really resolve the problem.
Dez getting injured is probably bigger issue than Safety and definitely a bigger issue than Nick Hayden getting injured.
I don't know if Jones will get reps at Safety in TC or not. If he does, then he would likely be the backup FS. Heath did start almost a full season. With a better pass rush and better surrounding players he could survive for a few games. The CB/Safety Corey White is another option. He has good physical ability. It's difficult to know if his issue with the Saints was RR's wacky scheme or something else. If Jones and Scandrick are the starting CBs, Carr might be an option to play some FS.
The have several options at DT. Hayden or McClain being out is not a big problem. Crawford being out would be the biggest issue, but if that happened after Hardy's suspension, they could use Hardy there on passing downs. Don't overlook Ken Bishop at the 1tech or Chris Whaley at the 3tech. Both have talent. Bishop was already strong than Hayden last year as a rookie from a tiny college. He is also quicker. He just needs experience. Whaley looked terrific in college game footage but fell though the draft because his injury would prevent him for doing anything as a rookie. They have a few other options. Jack Crawford's best game last season was at the 3tech spot. Coleman has really good talent but had issues being a professional as a rookie. Kracken has already been on him about being serious this off-season. Mincey can also move inside on pass downs.
All teams have some positions that are thin. Overall, at this minute the Cowboys have about as much depth as I can remember for any season. That could change if they have multiple injures in training camp, but as of this minute the depth looks reasonably good.