Do they recieve it on facebook?

[SparklyCupcakee]

If your not friends with someone on Facebook but you send them a message - do they receive it?

[Mitch]

yes.

[abraXus]

it depends on their settings

most people use the default setting, which means if you arent on their friends list, your message is put into their "other messages" folder (kinda like a spam folder) and they are not notified that it's there, so it is not very likely they will ever read it, unless they are the type of person who checks their "other messages" folder from time to time

[Samarth]

Remember to read this all, i typed all of this just for you-

a person whom you're not friends with will receive your message, if they have allowed it in their privacy settings. though, facebook is recently been rumored to roll out a new practice in which you will be charged if you send a message to someone out of your circle.
If they are your mutual friend (friend of someone you are already friend's with) you have high chances of having your message delivered.

[Angeleyes]

Yes that person will receive your message in their "inbox" or else their "other" folder.
Facebook also charges for messages to non friends so maybe it could be in archive or other.