With round core strings you need to make a 90 degree bend or crimp them before cutting. This will lock the windings to the core. The windings on round core strings don't lock onto the core like with hex core strings. If you don't bend or crimp the string the windings may unravel. Maybe not completely but it can still be enough to ruin the string. I discovered this the hard way with DR Hi-Beams back in the early 90s.
I must stress that the incident I described was a one-off. I had previously loosened TI flats on several occasions without any problems. Also, people sell TI flats used and if THAT works my problem was most likely a case of bad luck. Maybe I accidentally straightened the string to a position where the windings started slipping. Still, I won't risk doing it again so I won't be loosening my TI flats all the way ever again.
For what it's worth I've experienced something very similar with GHS Pure Nickels. All round core stings need the same precautions, not just TI flats.
It might also be worth mentioning that it's nearly always possible to adjust the truss rod on P-basses with access at the neck heel without removing the neck. I do it all the time at the workshop. There are several ways to do this, depending on the pickguard and the truss rod nut.
Scenario 1: Slotted truss rod nut and the pickguard has a cut out in front of the truss rod nut.
In this case can use a truss rod "cheater" tool but a small flat screwdriver often works fine too. Lots of people think you need a big philips screwdriver to adjust slotted truss rod nuts but the trick is to use a small flat screwdriver and insert it into one half of the slot. This will provide enough leverage (in most cases) and enough access without removing the neck.
Scenario 2: Hex truss rod nut and the pickguard has a cut out.
You can use a truss rod wrench with a ball end, like the ones from Fender (and come with all Fender USA instruments). You just angle it downwards into the nut. The only time I wouldn't use these is when the truss rod is extremely tight. In those cases you may need better access to fully insert the truss rod for a better grip.
Scenario 3: No cut out in the pickguard or if 1) or 2) for some reason won't work.
Loosen the neck screws just enough to be able to tilt the neck backwards. This will provide access for truss rod adjustment. It may be a good idea to loosen the strings a bit first but this will work fine without loosening the strings TOO much. I understand if this isn't something everyone may want to do, it can be a bit scary if you've never done it before (you really need to WHACK the neck to tilt it with the stings at tension) but I do it all the time and I've never experienced any problems. Another option would be to simply remove the pickguard screws and slide the pickguard a bit backwards to gain access. You will have lift the jack socket over the edge of the cavity and wiggle the pickguard over the pickups. It may seem like a lot of work but it really won't take much longer than loosening the strings and removing the neck. Just be careful not to scratch the pickguard under the strings.
All of these methods (except the neck tilt) will also give you the possibility to check your adjustments as you go. When you remove the neck completely there's a lot of guesswork and you may have to repeat the whole process if you don't get it right.
But whatever works for YOU of course!

Just a couple of hints that may (or may not) make your life easier.