Hi,
On a number of occasions I have seen badgers in chalk mines, but they only use tiny entrances from slumped-in levels. That is,
I got in through more open accesses and worked through long routes to get to where they were. They tend to fill up there holes to body-size by bringing in earth from outside, and construct piles of soil with nests in them.
They are very fearful, and tend to run away and hide, but I did meet one head on in the squeeze entrance to Clifford's Cave, Chudleigh, Devon, and it growled, beared its teeth and was pretty aggressive!
As for other animals, just plenty of toads feeding off flies feeding off sheep and dogs having fallen down shafts!
As one person commented, big cats should leave foot prints which would tend to be well-preserved undergound!
Regards,
D.Send.