Do restriction enzymes exist naturally in organisms?
Yes, that's where they originate from.....
Restriction enzymes (RE's) are among the most important tools in the defensive mechanism of bacteria and archaea. They are primarily meant as a defence against invading viral DNA (from bacteriophages like the T-range, M13,
Their own DNA , flowing loosely within the Cytosol, will be vulnerable as well but it will usually be protected from the action of the RE by Methylating a few bases so the RE can't latch on.
NOTE: the attachment site of a RE is not always the Palindromic site itself: some RE's recognise a different region, usually "upstream", where they seem to latch onto the DNA Helix, then make the cut in the Palindromic sequence.
But that is outside the scope of this question....