The standard input of background processes

[ievojeewai]

Perhaps this is a naïve question, but what is going on with the output behavior
differences with the example below?

    $ f()(cat); echo dramatic meow | f
    dramatic meow
    $ f()(cat&); echo furiously green | f  # no output
    $ echo trebuchet rockets | (cat&)
    trebuchet rockets
    $ f(){ cat&}; echo drop that eel | f
    drop that eel

I am failing to understand some interaction between functions, subshells, and
how stdin gets set on background processes.

Note that in dash, only the first example produces output, so it appears that
_all_ subshells fail to inherit (a copy of?) stdin in this case. Is this
perhaps specced in POSIX.1-2017 somewhere?

Any pointers in the right direction would be much appreciated.