There's a fantastic book written by a man who spent 76 days at sea. He floated in a raft, purifying water and eating what little fish he could catch.
At night, he couldn't see or hear the sharks. But he knew they were there from the hard bumps they'd give the raft.
No motor. No communication to anyone. Just endless black sea and sky, while sharks kept him up at night.
There was a guy who made it 76 days in the Atlantic and he happened to be a bad ass survivor type. His sailboat got RAMMED by a WHALE (that was a TIL for me) and capsized but he had a life raft.
The book is called Adrift and it's a quick read.
But it goes deep into all the things he had to do. Solar stills were the main reason he didnt die, also he caught some huge fish (Dorado) and made fish jerky. I think there was a mild shark attack as well.
hand pump reverse osmosis seawater filter for your life raft is the best answer
>We could try to set up an evaporation filter to remove the salt from the seawater, but we'd still have to sanitize it somehow,
https://www.amazon.com/Adrift-Seventy-six-Days-Lost-Sea/dp/0618257322/
Steven Callahan used inflatable solar seawater distilling things. You don't need to sanitize after distilling because viruses, bacteria and protozoa will not transfer over to the condensed water vapor.
That being said, Steven has since redesigned his life raft to include a rudder and a sail so he could self rescue instead of having to wait until you drift all the way to the tropics. I'm sure he has a modern reverse osmosis seawater filter too, now that they're available.
(personally, I'd also include a 20 meter QRP CW rig and a solar panel.)
I picked up the book at a used book store, it is well worth a read. Amazon link was de-crufted and offered for reference purposes only.
Adrift: Seventy-six Days Lost at Sea is my favorite.
Adrift: Seventy-Six Days Lost at Sea is also a great one. If you got frustrated watching All is Lost, you'll love reading Adrift.
Adrift: Seventy-six Days Lost at Sea - not to scare you, rather to prepare you.
For non-fiction: Adrift
http://www.amazon.com/Adrift-Seventy-six-Days-Lost-Sea/dp/0618257322