Depending on the parent, concatenation of finite and infinite words works or leads to an error
sage: W('1') + W('0')**oo
word: 1000000000000000000000000000000000000000...
sage: W = Words([0,1])
sage: W([1]) + W([0])**oo
...
TypeError: Python len method cannot return a non integer value (=+Infinity): use length method instead.