That seems to be a strange and debilitating bug indeed. I have not experienced that because I only use the app to make my moves and the app does not seem to be messing up. The browser messes up quite a bit. Chess.com told me in a support email that they were reversing games where this occurred, yet I don't know if they have done that nor how long they plan to do it.
"Frozen" daily games timing out without any chance to make a move

Thanks for the hint to the App: I've opened the game in question and it only shows an empty chessboard: No pieces, no information about players, no clock ...

Fortunately I witnessed this only once.
It was a vote chess game. In a promising position, we suddenly couldn't move any more and after a while we were told, that we had lost on time. But our administrator complained, and the game was again set in motion. 😊🙋

There's a known issue with Daily events that are from Custom positions and impacts some games from those events. Staff implemented changes that were meant to fix the problem, that went live a couple of hours ago, but I don't believe that fixed it.

@Martin_Stahl: Thanks for letting me know, that this bug is well known and long lasting.
Today it has paused all my daily games. If I make a move now, roughly three hours later the same game will trigger another day of vacation ... Sounds like some kind of fun which is worth to pay for, doesn't it?

+++ Breaking news +++ Correct position restored. Games still unplayable +++ Breaking news +++
Seen coincidentally, that the correct position in my frozen game has been restored today. Unfortunately the game is still unplayable as moves are refused as "illegal".
What about a contest for the "Bug of the day" ...?
https://www.chess.com/forum/view/site-feedback/contest-bug-of-the-day


After a week of forced vacation and seeing Chess.com inapt managing some help I'll try this now: I've turned off vacation manually, the "frozen" game should now time out in four hours.
I've created the tournament to which this game belongs to play some training games with friends starting with a particular opening. I've found two Fide Masters, who agreed to participate giving us a reference for games with the same opening against by far stronger opponents. One of several things, I better would have never tried doing on Chess.com.

Okay, I've learned one more thing: If I deactivate "vacation", that isn't accepted by Chess.com:
I've made a move in some games, resigned in some other ones and payed for this particular with another day "vacation" already after four hours.
Not only, that this annoying bug forces "vacation", there doesn't look to be any way to help myself. I've created this forum, filed a bug report, contacted two staff member personally. As I want to enjoy playing some chess, I'm probably wrong here.
Since at least two days there are "frozen" daily games. Here is my today's example:
As you can see, two moves are already made information on the screen doesn't fit at all: The last move shown in the list is 1. ... d5. Normally it should be white's turn.
Two days ago my opponent saw the same issue already in another game:
Listing shows 31. ... Kb5 as last move and after this white timed out. At first glance this looks to be quite normal, right? This is, what both players have seen right before the time out happened:
None of both could see the actual position ... here, which was still correctly shown in the list of current games of the black player:
I don't have any idea, how many games in these days time out without any chance for players to avoid this. Would be helpful to get some more examples ... Once these games will have timed out, everything looks quite normal.
Fun fact: If Chess.com's vacancies are still working correctly, I shouldn't time out tomorrow. Instead all my games will be paused and I still can't move in the one, which will cause the break.