Hi bdeslaur
I'm sorry you're having such a hard time

Not being sure if you mean you experience "pure" anxiety or anxiety with thoughts of "What if........" I'll give it a go from both sides, hoping that's OK........
Maybe brainstorm all the thoughts of "What if........." and list what you could do if each of these things were to happen (also considering how likely they are to happen on your lists!!) and for some things maybe your parents could give you ideas on what to do "if............" then maybe if you had an action plan for the "What if........"s that could reassure you a little...........??
And maybe you could agree with your parents specific times you can phone them, or them you, just to "check-in" for a bit of reassurance??
But before they will be leaving maybe you could plan what to do in that time e.g. if you have a favorite D.V.D. to watch, you highlight/save specific things on youtube to watch, short/easy things you might want to read..........so a list of things, although I'd say to make the list longer than it need be to fill the time as if you do get anxious concentration might be an issue and you might want to switch things. And maybe you could even find things on youtube that could help.........they have lots of relaxation music/clips on there...........maybe some "grounding" or breathing exercises...........
And maybe have something "productive" to do when your parents are out e.g. anything you can do in the home or write your parents a letter telling them...........sometimes it can be hard expressing feelings verbally.............and if you have a T or could get one..........or use helplines.........perhaps you could write down, ready to tell them, what some of the difficulties are.........
And if perhaps you could agree with your parents that they will go out for very short periods of time in between them needing to go for longer...........in a kind of "desensitisation" way.........for you to get a little more used to it??
And while they are out...........there is are chat rooms on here that might help as a distraction or for support..........I haven't tried them but maybe you could have a look??
Just wondering though if maybe a pet, however small, might help as a "comfort factor" when they are out??
Just some thoughts...........
Alison