I'm a big believer that you should have money available in the event of an unexpected financial emergency. Unplanned costs can take many forms. A medical emergency can present thousands of dollars in costs in one visit to the hospital. If your furnace or air conditioner goes out and the system needs to be replaced, you'll be looking at big costs.
Emergencies don't always present themselves only in the forms of costs. Cash flow can also present an issue. If your expenses stay the same, but the amount of money you bring in suddenly gets slashed, you can find yourself in trouble.
I believe that having an emergency fund can help address many of these issues, but there may be times where you need to go above and beyond what you have saved for such emergencies. It's prudent to have a plan in place in the event that you need cash even after your emergency fund has been depleted. Thinking about it now can make things a lot less stressful later.
Cutting expenses is a big option. If your bills go up or your income goes down, look at reducing your cash flow. Things that you may consider necessities may not be once you really find yourself in a crunch. Think about reducing or eliminating your cable bill. Cut your internet speed to the lowest available. Make sure you are paying the least possible for your cell phone plan. Cut or eliminate eating out. All of these things will reduce the amount of money you send out the door each month and can help you pay for that emergency, whatever it is.
Take on additional work. If you need to make up a cash flow shortage, consider looking at ways to increase your income. Taking on odd jobs can give you money here and there. If you're handy, try to see if you can get some simple repair or fix-it work. If you're great with computers, try to put that to use. Working a full time job, then taking on more work after isn't an ideal situation in the long run, but it can surely help button up your finances in the short term.
Look at loans. If you really need money, think about taking on a loan. The biggest thing to consider before asking for a loan or applying for a loan is to have a clear plan on how you would pay it back. The last thing you want to do is put yourself in a position where you get access to cash, but then don't have the means to pay it back. You can ask family or friends, though this can be uncomfortable and they may say no, in which case you should not be offended or let it jeopardize your relationship. Having a plan to pay back the loan will help.
The biggest takeaway here is to understand that an emergency fund, no matter how well stocked, does not provide assurances of guarantees. It's important to have an emergency fund as a buffer to unexpected costs, but it's just as important to plan beyond that.