According to a recent post on Pro Football Talk, rumors are flying that if the 8th Circuit upholds Judge Nelson's ruling granting an injunction, the NFL will respond not by opening its doors and beginning the new league year as we had all previously supposed, but instead completely shutting down. Their position would be that they would not be violating the Court's order, because there would be no lockout. They would then use this as leverage to force the players to agree to their terms.
I'm hesitant to believe the NFL would be willing to do something like this, for a couple reasons. First of all, it would be a public relations nightmare. As it stands fans seem to be about evenly split on the sides of the owners and players. If the NFL was seen to intentionally shut down the entire league and essentially go out of business, it would galvanize public opinion against them and cause a negative backlash. In the link above, Mike Florio seems to think they're OK with that, but it would really hurt their image with the fanbase, and people might be turned off. Enough to put a dent in the owners' wallets? I don't know.
Second, I'm not sure it would work. Courts don't look kindly at transparent attempts to avoid the spirit of their orders. The players could simply run back to court and ask the owners to be held in contempt, which they very well might be. Additionally, this would hurt the NFL's legal position in the future because they would appear to be acting in bad faith. Which they would be.
Whether this happens at all remains to be seen. Last week, the players were apparently bracing themselves for a full stay pending the outcome of the appeal, a sure sign the court was leaning towards overturning Judge Nelson's decision. That, however, hasn't happened yet. The Court could simply sit on the temporary stay until it decides the appeal. Right now, we just have to continue to wait and see what happens.