Quote from the OED [with my comments in square brackets]:
"Do not confuse
their and
there:
their is a possessive determiner, used for example in
they all tried to hide their faces and said nothing, [Air Force Board?]
while
there is an adverb of place or position, as in
I took a trip up there last week, and is used in phrases such as
there is/are: we are aware there are problems [but we won't do anything].
On the use of
their in the singular to mean ‘his or her’, see
they (usage)."
The grammar applies, whatever time of night it is, but is often affected by alcohol.
Rgds SOS