Re. contributions-based ESA (including based on national insurance credits whilst claiming benefits). This is not about UC. Therefore scroll on by if insufficient NI contributions and/or NI credits for contributions-based benefits.
My perspective/experience - I am on contributions-based ESA, and have been for about 4 years. Previously I was on ESA with a combination of contributions-based and means-tested. I am in the support group. No one seems to be interested in re-assessing me.
I think it's important to distinguish between what I'll colloquially call 'old' ESA and 'new' ESA. When the government and media talk about UC replacing six benefits with one, it's a load of twaddle - it's about replacing six benefits with three.
Let me take it back further to make it easier to conceptualise. Before ESA, we had incapacity benefit (contributions based) and income support (means tested) and you could get either one or both.
ESA replaced incapacity benefit and income support with one benefit consisting of two elements, contributions-based and means-tested, and you could get one or both.
Then along came IDS's super-duper UC. Oops! What do do with the people on contributions-based ESA? Quick, invent 'legacy' ESA which replaces the contributions-based element of ESA, which replaced incapacity benefit. Government information has now drifted across to calling it 'new-style' ESA. Well, mostly. Sometimes they call it 'old-style' ESA, but I think they're just getting muddled there and 'old-style' ESA is, erm, the old not-yet-transferred ESA, referred to elsewhere by the government just as ESA. Just don't get too nitpicky over their random press-release and politician soundbite jargon. I'm amazed I haven't yet heard any politicians referring to 'new-style old-style ESA'.
Another way I conceptualise the difference between what it gets called is 'ESA' = 'you're already on ESA and we haven't got round to transferring you to UC yet', 'new-style ESA' = 'claim UC, oh dear, you can't because you've got income/capital, so claim this out-of-date benefit'.
All such wonderful fun for claimants and DWP staff as we all play musical benefits and musical jargon. But in reality, it doesn't matter. UC's for those who haven't got much income or savings and ESA's for those that have and that have clocked up enough NI contributions or credits.
In my case, I had my contributions then had an inheritance and bye-bye means-tested element, just ESA (contributions-based). However, whilst some government stuff distinguishes between different sorts of ESA, my paperwork just says ESA.
Edited to add
I came back and edited this. When I first typed it, I'd checked on the .gov website and found the new sort of ESA referred to as 'old-style', but then I took another look and found that other .gov pages call it 'new-style'. So I've edited what I wrote, but the key thing is that I hope I've been clear that there's two sorts - the original one with two elements, plus (not replaced by) the newer one with just contributions-based element. If you look at any official guidance, take care when reading it and don't assume consistent jargon.
The other thing is that as a general principle my approach if the jargon in relation to anything official is inconsistent on official websites and reputable advice sites etc., I expect there to be a possibility of crossed wires when dealing with officialdom, so I tend to use descriptive phrases like "the sort of ESA you get if you've got national insurance credits and you're not eligible for UC".
The rest of my original post
As regards re-assessment, I haven't been re-assessed for ESA for yonks and my eligibility wasn't re-assessed when I lost my means-tested element. My PIP migration was about 4 years ago (the assessment started 10 months earlier!) and as yet no one's shown any interest in re-assessing me. I daresay they will once staffing numbers increase a bit and the government has another anti-benny-scrounger* binge. (* Other nasty insults for us are available. See tabloids or listen to politicians for latest versions.)
I leave it to others braver than me to make sense of UC.
*** Caution - what I say should be read in the light of anything Monic says, including any errors she may spot in what I've posted. I've never had cause to doubt what Monic tells us. Others also speak from their personal knowledge and experience and I do not claim to know better than them what they have observed. ***