ClearAll[Teacuppable]
TeacuppableHelper[set_List] := Module[{f, s},
  f = First[set];
  s = StringRotateLeft[f, #] & /@ Range[Length[set]];
  Sort[s] == Sort[set]
  ]
Teacuppable[set_List] := Module[{ss, l},
  l = StringLength[First[set]];
  ss = Subsets[set, {l}];
  Select[ss, TeacuppableHelper]
  ]
s = Import["http://wiki.puzzlers.org/pub/wordlists/unixdict.txt", "String"];
s //= StringSplit[#, "\n"] &;
s //= Select[StringLength /* GreaterThan[2]];
s //= Map[ToLowerCase];
s //= Map[{#, Sort[Characters[#]]} &];
s //= GatherBy[#, Last] &;
s //= Select[Length /* GreaterEqualThan[2]];
s = s[[All, All, 1]];
s //= Select[StringLength[First[#]] <= Length[#] &];
Flatten[Teacuppable /@ s, 1]