There are instances in which one spouse is the "breadwinner" of the family - and then abruptly leaves the marital residence and refuses to support the family. The remaining spouse should have a game-plan on what steps to take.
Consider filing a Spousal/Child Support action in Family Court
While often times if people are getting a divorce anyway, the knee-jerk reaction is to file for divorce. If there are emergency issues, however, such as how is the rent/mortgage going to be paid next month, then filing a motion in Supreme Court may not be the way to go. This is because Supreme Court is often slow in deciding such issues. Even on an emergency motion the court gets up to 60 days to decide the motion - and that's from when all papers have been submitted by both sides (which especially in NYC & surrounding counties can take 1-2+ months in itself). In other words, if you need a quick order, filing a motion in Supreme Court may cost you 4-5+ months just to get a decision - and even that's on an emergency motion.
You may proceed simultaneously in Family Court as well as Supreme Court in many instances
Generally the courts do not want the same issue pending in 2 courts at the same time. In other words, Judges would otherwise frown on the same party filing for divorce in Supreme Court & including a maintenance (i.e. alimony) claim in addition to filing a spousal support case in Family Court. However, one major exception is where the party requesting support is "in danger of becoming a public charge" - in other words, without the Court ordering the other side to pay support, the "needy" spouse would otherwise need to apply for some form of public assistance (food stamps, rent assistance, etc.). In Family Court, one can get an initial court date within 4-6 weeks of filing one's support petition - and therefore usually get some form of support order entered in far less time than it would generally take for Supreme Court to decide the support issue. As such, if emergency support is needed, the requesting party should strongly consider proceeding in Family Court first (of course after consultation with an experienced Family Law attorney)!