Check back your ace rag for hopes for a cheap showdown…
If we are in a hand with multiple checked streets and are in position with a weak made (like 3rd pair, 4th pair) and it again checks to us on the river, betting is usually pointless because any hands that we beat will just fold to the bet anyways and there are so very few hands ahead of us that might fold out. We will probably just win the showdown as is anyways. The bet risks losing more chips than we stand to gain.
So, no, just an ace rag in your holdings should be
Checked down, already knowing how your
Opponent plays. If you see a lot of his showdown
Hands, you can see if he is a calling station or
A bluffer, or if he is an honest player. If a player
Has a standard hand range, You will have
Better equity with an ace rag depending on his
Position. Lets say he is a positional player and
Rarely plays trash hands. Then yes, i would say
You can call with your ace rag on later streets
If he is out of position and he is known to be
A bluffer or aggressive out of position… but if
Hes loose any position, check down ur ace rag ,
Although he can bluff u off a river… there
Will be other times 
In the spot that I mentioned though, more often than not those pots are 3-way 4-way 5-way (because of the cheap flop and checking) so bluffing or betting evokes even less of a good idea and even then only if all Villains are of the same type, which basically never.
Heads-up, yes there will be spots where you can mix that in.