The happiest situation, of course, is when the collector has deserving and interested relatives and or friends who would appreciate and maintain the collection, but I fear this is not a common outcome.
Similarly, the vast majority of the items in our collections are unlikely to be of interest to museums for inclusion into their collections and display. They can only absorb so much.
This means that the majority of our collections will find their way back into the marketplace and ultimately into new collections as the cycle completes another turn. This is not bad as this is where most of our own collections came from.
Unfortunately, preserving the monetary value of the collection upon dispersal for the collector's heirs will be difficult if possible. When items have been held for a good long time and have not fallen from popularity (or have been wrongly stigmatized and blocked from sale as is the current case of items with ivory content in many jurisdictions) natural price appreciation and the background of inflation will mask the expenses and trauma of transfer.
Sale by auction has been favored in the comments above and given the correct venue and a decent turnout may be the highest yielding 'turnkey' solution. Still, for most items, auction prices are likely to lag behind retail gallery prices, partially because the buyer must account for an obscene 15 to 25% (or thereabouts buyer's commission) beyond what the seller's commission will take. In any case expect, on a 'good' day at auction, that something like about a third of the value will be absorbed by the transfer process. With penalties for 'high' reserves, setting a reserve can provide only so much protection.
Selling to a dealer is another solution that may provide a quick and relatively easy 'turnkey' solution. However, one reality that many collectors may not realize until they try to sell in bulk is that a buying dealer must tie up their capital in the collection and it may take a lot of work, ancillary expenses and years to sell. This means that one should expect only 25 to 50% of the price that the dealer eventually hopes to realize. As some of you recoil in horror, let me advise you (from my own adventures as a 'limited instruction set specialist antique dealer') that the dealer is very likely going to earn that markup. At least with this option your heirs do know what you will get 'up front'!
You, your family or a friend of the family can always try the DIY (do it yourself) option and work through the collection via online sales or sales at gun shows and achieve a low retail return if you have the time and patience. You will surely earn the improved return with many hours of labor and you should go into such a plan with your eyes open as to issues with online sales hosts and their policies that may leave you hanging or 'crushed under the bus'.
Our deceased forums moderator Lew Waldman left his family with a written ledger book for about half of his
collection with inventory numbers, a description and some of his thoughts about each item and an estimate of value. Doing so has increased their recovery of his collection's value. A database is great for the collector (and Fernando has covered what needs to be included above) but I would advise there also being a paper copy of the information just in case the family is less computer adept or the password for the well-encrypted file dies with you. (After all the file includes the greatest secret a collector will likely have kept from their loved ones - namely how much they have invested in their collection!) I have no one to keep this information from, and yet I still greatly restrict its dissemination. I have sternly warned my next of kin to find my records before disposing of anything - whichever option you choose they will need to have this information to intelligently assess their options! So, perhaps a private (only your name and signature) safe deposit box for your records of provenance, receipts, etc. and only a note they will find telling them where to find the key once they have a death certificate to present with it at the bank.