For a little while now a fight has been brewing in Ashdod. The BIG mall in Ashdod decided to open on Shabbos, to the chagrin of the local religious community, especially the significant Haredi community there.

There have been threats of bans, attempts at political pressure and other methods of intimidation to get the mall to close on Shabbos. So far the mall remains open.

The Badatz has now issued a letter prohibiting people form shopping in the entire BIG chain of malls, along with a prohibition against investing in the company. As well, those already invested must withdraw those investments, so as not to be a part of public chillul shabbos..

The letter has yet to be publicized, due to continued attempts at persuasion.
source: Bechadrei

I would note that this is what happened way back when with Shefa Shuk. The owner of Shefa owned a separate chain of markets which were open on Shabbos, so the Haredi community threatened to boycott Shefa Shuk as a way of applying pressure.

The boycott was never issued, but the letter kept in the safe became a de facto ban, as large parts of the community stayed away from Shefa, at least for a significant amount of time.

The publication of the existence of such a letter being ready might be enough to cause BIG a BIG problem.

The question I have though is what to do in other places where BIG is careful about Shabbos, even if they really would prefer not to be - should they be banned as well? Would a ban possibly encourage other places to open - after all, they are killing themselves to stay close don Shabbos, but get banned anyway!

I am thinking of Bet Shemesh as an example. It was not really BIG, but one of the resident businesses of BIG in Bet Shemesh stayed open for years on Shabbos. Recently they succumbed to the persuasion and shut down. If BIG will be banned by the local community anyway, even with them having given in and agreed to stay closed on Shabbos, maybe they will reopen, as it is almost pointless to stay closed, in their perspective.

The situation in Bet Shemesh might be more complex than just that, as it was only one shop, and maybe they've decided it is more financially beneficial to stay closed and have kashrut then to remain open with no kashrut. However, it is possible this will affect the decision. There might be other places that will react poorly to a general ban and stores might decide to open...