I am more of a lurker, but since I have noticed the "Tent smashed by tree" post across a few different subs. Here is how I have always slept in a forest.
Next to a log that has been there for a while and won't be moving anytime soon, and if you are concerned just take the uphill side. If you are lucky enough you can sleep in-between a few deadfalls if you are in a real matchbox situation like I was a couple weeks ago in the Targhee.
If a tree falls you are protected, and they also keep the wind off ya... Just watch out for termites in the warmer months, they may interrupt your sleep, but you can snack on em: "Lbs for lbs more protein than chicken or beef.'
A thunderstorm came that night and the only thing that disrupted my sleep was heavy rain on my Basha, thunder, and later on some wolves howling... There could have been a few trees crashing as well, but they may have thought nobody was around (due to the camo) so they didn't make a noise.
TLDR: Stay safe sleep with a tree
Edit:
I didn't mention it, but the Rifle and the Orange Hat were clues that I was hunting, and I assumed folks know how backcountry hunting works and that's my mistake, we all come from different backgrounds and yeah, my bad.
While hunting the Animal often dictates my camping area, and hunting goes until it is dark outside. I can check my map and see where the closest ideal campsite would be, but backcountry means back-frickin-country, 4 miles from the nearest trail and there was also a storm coming in. Instead of taking the risk of blowing my 9 days of previous hard work on that hunt or bushwhacking in the dark which isn't the safest bet in Grizz country, I chose to sleep in a matchbox of deadfalls and a mix of live and dead standing trees in a 50 year old burn. It is not ideal, if I was hiking the PCT or the AT I would just trudge on a couple miles and set up camp in a safer spot, but this is wilderness backpacking I am sure many of you go miles off trail and get where I am coming from, but I would still sleep next to a log in a forest when given the option, it's safer than nothing and blocks wind reflects body heat better than air.
Bivy bag, freezing temps, and possibly my smell after 9 days also means that bugs and snakes don't mess with me sleeping on the ground, I have never had an issue above 5k feet in the fall-early spring, if you haven't tried it, sleeping on the ground is "the way."