joining adjacent elements by rule

StringJoin /@ SplitBy[lis, DigitQ]

yields:

{"a", "1", "cefg", "2"}

You can also use SequenceReplace:

ClearAll[sR]
sR = SequenceReplace[{p : __?(StringMatchQ[LetterCharacter ..])} :> StringJoin[p]]

or, a variation on ubpdqn's approach, using Split:

ClearAll[splitAndJoin]
splitAndJoin = StringJoin /@ Split[#, Nor @@ (DigitQ /@ {##}) &] &

Examples:

lis1 = {"a", "1", "c", "ef", "g", "2"};
lis2 = {"a", "1", "c", "ef", "g", "2", "345", "A", "B"};

sR /@ {lis1, lis2}

{{"a", "1", "cefg", "2"},
{"a", "1", "cefg", "2", "345", "AB"}}

splitAndJoin /@ {lis1, lis2}

{{"a", "1", "cefg", "2"},
{"a", "1", "cefg", "2", "345", "AB"}}

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