I need a tooth extracted. What will happen to the empty space if I can't afford an implant or bridge?

With missing teeth. The other teeth will tend to shift into that space over time. Short term (1-2 months) it's not a problem but long term it is. This creates more stress on the remaining teeth as well as more likelihood to develop cavities & gum problems. Discuss options with your own dentist. Some missing teeth are more important to replace than others. See if you can work out a payment plan or flexite partial.
Removable partial . You can replace your missing tooth with a removable partial or a flipper. This would be a more affordable option and is better than leaving a space. Talk to your dentist about all of the options. If you have a dental school or a hospital training program in your area talk with them and you may find lower fees so maybe even the implant can fit into your budget.
It will remain empty. It will remain empty withot a tooth visible there.

Related Questions

Need a tooth extracted due to impaction. Teeth are rather crooked. Can I get an implant or bridge instead of braces? Can a spacer hold the spot temp?

Depends. Depending on the space between the teeth and the position of the tooth roots, dental implants may or may not be an option. A dental bridge may also be possible. If braces are what you truly want, often times an appliance could be made to maintain the 'open' space until you are able to have the implant placed. This will prevent unwanted tooth movement. Read more...
Bridges can... Help align the teeth to be straighter, but there are limitations. I would consult with your local dentist to get his/her professional opinion regarding your specific case. Read more...
Consider both. Not seeing your problem, can't give definitive answer. Best to consult with your restorative dentist and an orthodontic specialist. Learn about all the options available to you, then pick the one that will give you the best bang for your buck. Good luck. Read more...
See a dentist. There are many questions that you present that cannot be answered without x-rays, a bite alignment evaluation and a thorough exam. I would even possibly get a couple opinions to help you hopefully decide which direction to take. Read more...