Variable length Fibonacci word
Haskell, 15 bytes

a#b=b++b#(a++b)

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Takes strings a and b as input, returns the whole infinite Fibonacci word, as is usually allowed in sequence challenges.
How?
Not much to say. This answer relies on the identity
$$
F(a,b)=b+F(b,a+b),
$$
where \$F(a,b)\$ is the infinite Fibonacci word with starting words \$a\$ and \$b\$.