SSD can run just fine on sata 2. You just get a speed penalty off cause over sata 3. i have run like 6 sata SSD´s from Samsung and crucial on sata 2 and sata 3 on my old X58 system and none of them have ever failed. I have so far never had a SSD failing on me and i have run SSD since like 2011. I will say its more about that are the given sata SSD backward compatable with sata 2, if not you might get in trouble.
In short your max speed get limited to the half of sata 3 with sata 2. You will go from a max speed on sata 3 of 585 MB/s read/ride to sata 2 that is around 285 MB/s read/ride. But if you are coming from an HDD as OS drive to an SSD as OS drive. You will still get a huge difference in speed and how responsive your pc is.
Here are some test i dit with Samsung EVO 850 250 GB and Crucial MX300 275 GB on sata two. Its the result to the left, that is the SSD test. On the right side is just two WD velociraptor in raid 0 while i had those two.
This is on my newer laptop with an M.2 Sata SSD runs on sata 3 interface. Its a cheap SSD, so deffently not the fastes SSD out there, but it can give an idea of the speed loss from sata 3 to sata 2.
Here is my older Samsung 950 PRO NVMe M.2 SSD running on my X58, for those that might want a fast boot solution on an old pc. Its really nice with an NVMe SSD even throw this one is an older one nowm but still far better than any sata 3 SSD.