This article from James Allen explains very factually what is happening with StefanGP, the team that has no Formula 1 grid slot for 2010, but is acting for all the world as if it does:

“Stefan Grand Prix writes history! SGP becomes the first team in F1 history who did send a 40 foot container full of equipment to the race in Bahrain without having entry for 2010 season!” said a statement.

Leaving aside the slight English roughness, this is one of the great unrealized stories of the 2010 season. Why would a team that has no F1 entry (it was refused last Summer, and that remains the case despite threats of legal action by the team at the time) be spending millions of dollars on a car, freight, personnel etc. to test at a faraway circuit?
The answer may partly lie in the rumors that Campos Meta, one of the contracted teams, does not have the money to even build its car for 2010, much less go racing. Rumor has it that Tony Texeira, the CEO of A1GP, has already offered to buy the team off of Adrian Campos. However, that is not likely to be greeted with cheers inside Formula 1, since A1GP is insolvent and apparently owes Ferrari (the engine supplier for the series) a seven figure dollar amount.
Part of the full answer may lie in the behaviour of Toyota in all of this. It is already known that the StefanGP car (chassis and transmission) is the design that Toyota would have raced in 2010 as the TF110, had they not decided last year to withdraw from F1. Now there are rumours that one of the StefanGP drivers will be Kazuki Nakajima, who was a Toyota-supported driver at Williams GP for the last 2 seasons. In addition, Toyota is known to be providing all sorts of engineering support to StefanG, including supplying the engine, which is essentially the Toyota F1 engine from last year, rebadged.
There is a thread on the unfolding story here and here.
All of this leaves me wondering whether Toyota has decided to keep a presence in F1 in case they want to return when the economics make sense for them to return. This is similar to Honda, who withdrew from F1 in the early 90's, but retained an engineering presence via their Mugen subsidiary, and Renault, who withdrew after 1997, but retained an indirect engine supply presence via their Mecachrome subsidiary. Another factor to consider is that Toyota may have signed the post-FOTA contractual agreement to compete in F1 until the end of 2012, in which case they would have faced stiff contractual penalties for withdrawing. Their supply of resources to StefanGP may be a way of avoiding litigation.
The full answer, as is always the case in F1, is probably not simple. It is probably a combination of three or more of the following reasons:

1. StefanGP may have had a credible threat to go to the EU over the F1 team selection process from 2009. There were numerous complaints from other prospective entrants such as ProDrive that the FIA was demanding all sorts of concessions from applicants (including, in one case, that all new teams had to sign an engine supply deal with Cosworth). This might well have been frowned upon by the EU.
2. Toyota wants to avoid litigation resulting from their withdrawal from F1 after signing the new commercial agreement.
3. Toyota wants to keep its seat warm in F1, in case it decides to return in 2-3 years' time. Providing support to another team would be an ideal way to do this at arms length, to at least maintain presence and contacts within the sport.
4. There is a genuine belief that Campos Meta (at least) will not be able to compete in F1 in 2010 because of lack of money. StefanGP would be an ideal short-term replacement

Against this, it must be pointed out that the StefanGP team will be short of track time even if they do get an entry, and even if the FIA allows them to join after the start of the 2010 season. The team does not currently have an announced tyre contract with Bridgestone, so it is not even clear what tyres they would use for testing, although, as a team not entered in the 2010 championship, they would not be bound by the current F1 testing restrictions, which might make them attractive to either Bridgestone (for extra tyre testing) or even to a new tyre supplier for 2011 and beyond.
There is also evidence that the Toyota F1 engine was probably the weakest powerplant last year in terms of horsepower, and being an engine that is already homologated, Toyota cannot rework its design except in a very limited way with the agreement of other suppliers to address reliability concerns. It is therefore unlikely that StefanGP would be anything other than a grid-filler team, at least in the first season.
However, this current series of events is proof that in F1, nothing is ever simple...