Is the marriage contract of the questioner's sister considered void if her husband is a perpetual disbeliever—Allah forbid—and he is aware of the ruling on disbelief, while they reside in a foreign country that prohibits judicial separation? And what should the questioner do regarding this matter?

A person is not to be declared a disbeliever unless the conditions are met and the impediments are absent. Furthermore, proof must be established and doubt removed. If your brother-in-law utters something that expels him from Islam, advising him is obligatory. If he does not repent, the matter should be referred to Islamic centers. Advising and denouncing evil are obligatory to the extent possible, while denouncing it by heart remains an obligation in all circumstances.