Money orders effectively work like prepaid checks, so if one is lost or stolen, you will likely want to replace it quickly so it can't be cashed and you're not out the money. The U.S. Postal Service and other organizations that issue them will let you replace a lost or stolen money order for a fee and will add your money order to a list of missing ones that cannot be cashed. They can also replace physically damaged money orders.
TL;DR (Too Long; Didn't Read)
If a postal or other money order is lost or stolen, contact whoever issued it as soon as possible to have it replaced and flagged as missing so it can't be cashed. You may need to pay a fee for this service. If a money order is physically damaged, you can also usually have it replaced.
How Money Orders Work
The U.S. Postal Service and private organizations like Western Union can issue money orders, which are cashed or deposited like checks but are prepaid rather than linked to funds in a bank account. They charge a fee for doing so, depending on the value of the money order and whether it is being sent to the United States or another country.
Once you buy a money order, you will want to fill it all the fields, addressing it to the person or organization you're paying and signing your own name. Remember that if the money order is stolen before you address it, a thief could write his own name on the money order and cash it, so you will want to do this quickly.
You'll also usually receive a receipt with your money order which you should hold on to in case you have any issues. When someone receives a money order, he or she can usually deposit it at a bank or cash it at a check cashing location or post office.
Lost or Stolen Money Orders
If you send someone a money order and it doesn't arrive or is otherwise lost or stolen, contact the organization that issued it as quickly as possible, whether that's the U.S. Postal Service, Western Union or another institution. You will want to have that money order replaced so a thief can't fraudulently cash it and so that you can get a proper money order to the person you're sending money.
You will generally have to pay some sort of fee to have the money order replaced and usually fill out a form. The U.S. Postal Service will add your money order to a list of missing money orders to prevent it from being cashed.
For Western Union money orders, you will usually have to pay a higher fee if you don't have the original receipt.
Damaged Money Orders
If a money order is physically damaged or somehow defectively printed, you can have it replaced. Contact the organization that issued it to explain the issue and exchange it for a new, undamaged one.