What I like to do, and have been doing for years, is the following. Worked great even in Utah camping directly on slickrock – in lots of places there the "soft" stuff is off limits because of the exotic cryptobiotic soils.
I always make sure my tarp lines are extra long. There are multiple version of this depending on the types of loop you have on the ends of your lines. For the the sake of an argument lets assume you have fixed loops tied for your stakes. You can easily imagine generalizations to other types of ends.
So, you already have the loops in the ends of your lines, but your stake are now useless. If you have rocks within a 100 yards of you campsite then go and find some reasonably heavy ones that have a diameter of 1-1.5 feet. Flat but heavy are ideal. Make a "lasso" loop by pulling the guy line through the existing loop and wrap around the rock. Cinch tight, and start rolling the rock (or flipping it to adjust the length and further wrap the line to the rock. This last is not strictly necessary but allows you to adjust the length of the line to your preference. Either way you move the rock to make the line tight, and to put it in the right spot. Place rock were a stake should have gone. Rinse and repeat. Pile more rocks on top of that rock if a gale is coming. Works equally well with logs so long as the have something sticking out that keeps them from rolling. Use common sense in this.
This is much easier than the pile'o rocks with a stake buried in it method, but depends on finding rocks of the appropriate size. Also much easier to fine tune. Also does't require any fancy rigging at the end of a long day, but does not rule it out in a pinch.
It you are out of rocks, and don't have a jackhamer, you may be SOL. Very unlikely for all those situation to be met. Ive never had it happen.
Edit: of course regular "camping spots" are the worst possible case. Not just because the ground is often compacted, but extra logs and rocks may either have been picked clean, of may be off limits. Yet another reason to avoid them when you can.