Stream.collect implementation not only creates a new FuncStream, it mutates an original stream.

routine.sc

(
var a, b;
a = Routine.new({
	inf.do{ |idx = 1|
		idx.yield;
	}
});
b = a.collect({|item| item * 2;});

b.nextN(10).postln; // -> [ 0, 2, 4, 6, 8, 10, 12, 14, 16, 18 ]

a.nextN(10).postln; // -> [ 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 ] WTF?!?
)

I found an old thread where James McCartney explained a reason of why routines could not be copied.

It would mean copying the entire call stack. Since you can non-local return out of a Routine to the parent thread, it would mean copying the parent thread(s) call stack(s) as well. Otherwise, loop counters, instruction counters, stack pointers, etc would get very confused if a frame were re-entered twice. So multi shot continuations are not easily possible.

sc-dev: strange stream embedding behaviour.

Another observation: shallowCopy worked in my previous example because b was created before a was started. Otherwise shallowCopy would simply return a reference to a (at least, it seems so). That also makes sense, considering the quote of James McCartney.