Is there an underlying SDP entitlement?

A little bit of a complicated one…

Client is in her late 50s, has learning difficulties. She gets enhanced PIP care. A few years ago she lost her cleaning job and her support worker helped her claim ESA. At the time she had savings over £16,000 and was awarded cESA support group. When this was renewed the client got no points and lost her ESA award.
I took the client to appeal and at the end of last year she was placed in the WRAG group.
Her savings are now under £6000.
DWP are saying she has to move to UC because her 365 days of c-ESA have run out. I am unclear as it seems to me she should still at least have underlying SDP entitlement but possibly I have misunderstood the rules? Can someone help me make sense of this?

She should have been receiving irESA with the SDP from the point at which her capital fell below £16,000. This is because old-style ESA is just one benefit and there is no barrier to switching from cESA only to cESA with an irESA top-up and then onto irESA as circumstances dictate.

I am assuming that the reason that she is not already getting irESA is because she hasn’t told DWP that her capital is now below the limit. I would suggest doing that immediately. Hopefully it might be possible to salvage some amount of backdating.

I think it is important to establish if her savings were below £16000 before any entitlement to cESA exhausted? Then as Elliot mentions see if backdating can be applied.