Problem: Spammers are creating accounts to post links in inboxes.
Solution: Add profile option to make the inboxes of users excluding mods and admins not message-able unless you are friends with the user; this should be turned on by default so the site isn't blamed for the user's choices. Mods/admins would have to keep theirs message-able in case a new user or non-friend needs to contact them, so making this feature disabled for mods/admins would be necessary for site moderation and communication.
Benefits: Spammers would no longer be able to message inboxes unless you the user actively permit them to. This would remove some blame from the site while providing more choices for the users to take advantage of.
Downsides: Users would be unable to message people directly if they are not friends, which would force users to either follow each other or give up trying to message someone's inbox. This would disable inboxes as a medium of communication for non-friends, hindering overall site communication. However, messaging between non-friends would still be possible in threads and walls. Again, this should be disabled for mods and admins due to the need for communication with said individuals for reports and user needs.
Potential Issues: Spammers would likely shift their tactics to comment sections, profile walls, and threads. However, this would represent a first step to cutting off the ability for spammers to freely spam people. Future steps could build off of this, gradually blocking off the holes in the site's security against spam.