canonical[list_List] := Last@Sort@ Flatten[NestList[Reverse /@ # &,
                                 NestList[RotateLeft, list, Length[list] - 1], 1], 1]

nonCanonicalQ[vals_] := (vals != canonical[vals])

nonCanonicalQ[{5,4,3,2,1}] (* False: means that it's a canonical list *)
nonCanonicalQ[{3,4,5,1,2}] (* True: means it's not a canonical list *)

sysDAE0 = {s[1]'[t] == 0, s[2]'[t] == 0, s[3]'[t] == 0, s[4]'[t] == 0,
      s[5]'[t] ==  1, {s[1][0], s[2][0], s[3][0], s[4][0], s[5][0]} == {4, 3, 2, 1, 0}}

{solDAE} = NDSolve[{sysDAE0}~Join~{WhenEvent[Evaluate@nonCanonicalQ[varsOt],
  "StopIntegration"]}, vars, {t, -1000, 1000}];
solDAE = vars /. solDAE

nonCanonicalQ[Through[solDAE[0]]] (* False *)
nonCanonicalQ[Through[solDAE[100]]] (* True *)