The Pagat site is very useful:
http://www.pagat.com/boston/solowhist.html It explains the main game "Solo Whist", and also lists some minor variations, and other similar games in this "Boston group".
They say that it is mainly played in Britain.
Here in Australia we also play it.
Solo Whist was taught to us as children to introduce us to card games, and has held us in good stead for Bridge.
Regarding the "Prop and Cop": We believe that that is an important aspect of the main game.
We do have that bid, and we find it to be very enjoyable.
It is an opportunity to collaborate as two teams, rather than three people collaborating to defeat the solo declarer.
If a Prop-and-Cop does not eventuate, then we also sometimes do the "Goulash" deal.
boardgames.stackexchange.com/users/12778/David Crossley
See Wikipedia's page on trick-taking games for a lot of variations.
The version you mention could possibly be Spades .
boardgames.stackexchange.com/users/11743/AndyT
We have a variation regarding the dealing:
We deal in clumps, i.e. one round of four, and three rounds of three.
We allow the dealer to do whatever order that they want.
Some try to get fancy regarding when they deal each four (e.g. different for each round), while most just start with a packet of 4 (i.e. 4,3,3,3) so as not to confuse themselves.
The Pagat and Wikipedia descriptions involve a single deck and use the final card of the dealer face-up to determine the trump suit.
We instead use a second deck.
This is then ready to go for the next game, being already shuffled and so just needing to be cut.
So the game should be faster.
This also means that the dealer does not need to expose one of their cards.
boardgames.stackexchange.com/users/12778/David Crossley
We have a variation which we call " Nash Whist ".
(Disclosure:
Our group of players has been refining "Solo Whist" for many years.
I have documented our version at the linked location.)
We have streamlined and simplified the shuffling and dealing (as described in the earlier answer).
In the original game the bids are limited.
Apart from the Misere bids, the solo bids are Solo (five tricks) and Abundance (nine tricks) etc.
This means that the main bid that occurs is Solo, and you also get paid for any "over-tricks" that you manage to make beyond the five.
For Nash Whist, we added other bids at every level from 6 to 13.
We also added rank of suits, as for Bridge (explained below) and No-trumps.
Apart from the normal Prop-and-Cop, the minimal bid is the normal "Five-in" solo, i.e. play alone against the other three with the initial turned-up suit as trumps.
So win five tricks in the indicated trump suit.
The trump suit can be changed by any bidder when it is their turn to bid.
Higher bids will beat the previous bid.
For example "Seven-Out" in any suit will beat "Six-In" (i.e. Six in trumps) and Seven-In will beat Seven-Out.
The rank of suits is as for Bridge (i.e. Spades is highest, then Hearts, Diamonds, Clubs).
For example, if Hearts was turned up trumps and the current bid is Six-In, then a bid of Seven-Out Clubs would beat that, and a bid of Seven-Out Diamonds would beat that.
Note that a bid of Six-Out Spades does not beat Six-In, because in this example Hearts are trumps and so automatically rank at the top.
The bidding can start at any level, and proceeds with higher bids until no-one wants to bid further.
The last bid is the "declarer".
Their suit is now Trumps.
There are no payments for over-tricks.
This encourages people to bid to the limit of their hand and not be safe.
boardgames.stackexchange.com/users/12778/David Crossley
We have a three-handed variant.
We simply remove the whole Clubs suit.
No Prop-and-Cop.
Misere is difficult and often does not occur, so we add a "Triste" bid below 8-out, allowing one trick to be won.
Everything else is the same, just need to modify some guidelines for hand-assessment and play.
boardgames.stackexchange.com/users/12778/David Crossley
This was the second trick-taking game that I learned as a kid and it involved bidding and gambling (we played for tiddlywinks). Needs 4 players and you can play to lose. It was used as a  training-wheels simple introduction to the concepts of contract bridge (my dad was a bridge-player).   Since childhood, I've never heard of anyone else playing the game - is it known as something else? I've found it in the odd card game book, but the rules were slightly different to what I recall.
What variations are there on Solo whist?
boardgames.stackexchange.com
<solo-whist>
boardgames.stackexchange.com/questions/22581
boardgames.stackexchange.com/users/11561/Dave45
There are many variants including Solo Whist, Nash Whist, using a second deck or a third hand. The website http://www.pagat.com/boston/solowhist.html explains the main game and lists some variations. You can deal in clumps, i.e. one round of four, and three rounds of three or even use a second deck. You can play where the trump suit can be changed by any bidder when it is their turn to bid, or have a three-handed variant.  
The website http://www.pagat.com/boston/solowhist.html explains the main game and lists some variations. You can deal in clumps, i.e. one round of four, and three rounds of three or even use a second deck. You can play where the trump suit can be changed by any bidder when it is their turn to bid, or have a three-handed variant.  