ClearAll[f1, f2, f3]
f1 = Cases[{___, {Except[a_]..., a_, Except[a_]...}, ___}]@*Cases[{___, {(a_)..}, ___}];
f1 = Select[MemberQ[Tally /@ #, {_, 1}, All] &]@*Cases[{___, {(a_)..}, ___}] ;
f2 = Pick[#, MemberQ[#, {_, 1}, All]& /@ Map[Tally, #, {2}]]& @*Cases[{___, {(a_)..}, ___}];
Examples:
lst1 = {{{4}}, {{7, 7}, {7, 7}}, {{5, 5}, {6, 6}}, {{2, 1}, {1, 1}}};
f1 @ lst1
{{{4}}, {{2, 1}, {1, 1}}}
f1 @ lst1 == f2 @ lst1 == f3 @lst1
True
lst2 = {{{3, 3}, {3, 2}}, {{1, 1, 1, 1}, {1, 2, 3, 0}, {1, 0, 0,
0}, {1, 0, 3, 2}}, {{1, 1, 1, 1, 1}, {1, 4, 3, 0, 4}, {1, 3, 3,
3, 0}, {1, 0, 3, 4, 4}, {1, 4, 0, 4, 4}}} ;
f1 @ lst2 == f2 @lst2 == f3 @ lst2 == lst2
True