Surely your fellow collectors can be relied upon to leave your specimens undamaged and in your possession! Well, not always... There were rumors in my youth about an esteemed professor -- now long deceased -- being searched as he left a country, with the search revealing several important specimens from the country's national collection. And some people are accident-prone. Most of your fellow collectors are undoubtedly honorable people, but if you don't want to suspect your fellows, and wish to prevent mishaps, there are some things you can do to protect your collection.
When showing your collection to a group, only show it in closed cases. You can open a case to hold up (or pass around) a specific piece, but don't leave people with unsupervised access; they might knock something over.
If you are showing your collection to an esteemed guest, let him or her ramble with you at their elbow to explain, describe, and tell stories about your wonderful specimens.
Trades have two sets of hazards. You may get the worst part of the bargain, but that is an inevitable part of a collector's education. Learn from your mistakes.
The second hazard lies in the exchange circumstances. Pack any specimens to be mailed securely. Be prepared to deal with the circumstance that your trade partner's specimens may get damaged, and have an agreement in place as to how the two of you will deal with damages or mail losses. You may want to send things using a secure form of transportation, such as registered insured US Mail.
When you loan pieces, the loan is usually for a display or to a museum. A loan should have a clear description of who is responsible for transporting the piece, and a clear notion of the duration of the loan. Many museums have special loan paperwork. Also think about security and insurance for your loans. If something happens to the destination site -- a theft, a fire, etc. -- you should be able to demonstrate that the item in question belonged to you.
Sometimes items are sold or traded on approval; again, have an agreement in place in writing before you send out an item.
The purpose of written agreements is to make a trade, loan, or other deal run smoothly when unexpected events occur.