The answer to your last question really depends on the court schedule and whether you could get an emergency hearing.

There are some cash emergencies I can help with by disbursing funds early through escrow.

Likely you will get high quotes due to the emergency situation.

If so, I would recommend trying to cut expenses, making sure you have an emergency fund, paying down any debt and saving for a down payment.

You also need appropriate language in your lease or house rules to authorize (and reference) these fees.Examples could include- auger toilet; rekey locks (per cylinder); painting (per room, or SF): cleaning appliance; stripping/waxing per room; carpet shampoo per room; light cleaning; heavy cleaning; trash removal per pickup load...You also need an adequate disclaimer for NON-routine situations- perhaps an hourly charge, or emergency after hours rates, etc.

One lady broke her lease for a family emergency.

If it is an account that is more or less a necessity (like phone service or car payment or utilities), then that is s bad indicator; if it is for more of a luxury or extravagance or non-necessity (say a department store charge card), then you might be more willing to overlook that; if it is for medical related expense - well, if somebody had no health insurance and required an emergency room visit, that can be a big bill and likely to go unpaid, but one of those things that you should consider ignoring.

Will I have enough reserves for an emergency? 

I had one tenant who was called back to London in an emergency with 24 hour notice.

If you look at real estate investing where your properties exists within a wider community, where rules are made so all can enjoy the area, maybe you'll look more favorably on those hard nose bureaucrats.And then in the neighboring suburban areas, where for years they resisted adding units to SFR which is what these areas are zoned for, they now allow adding mother/daughter units where folks could house aging parents an emerging problem.