as in, "the A.R. delayed raising the flag until (s)he saw that the
offside-positioned player was actively involved in play".
Admittedly, possessive pronouns can't be neatly fudged together, i.e.
"his" and "hers" don't play together well as either "(s)his" or
"(h)hers". NO MATTER! In our people's collectivist paradise, we are
all one together and all property is communal; therefore we simply
avoid using gendered possessive pronouns altogether in favor of
neutral ones e.g. "the" flag. However, it is also my duty, comrades,
to advise you that the people's collective has assigned me the task of
being guardian of a set of roto-flags, so don't get any ideas of going
into the equipment bag the collective also assigned me, or (s)he is in
for internment in a re-education camp.