Car repair taking more time is it okay to leave car idle at dealer's place

If the dealership is holding it I would not worry, If something does happen to it, they are the ones liable for the problem.

Thanks Steve.
Let's say I am getting my car after a year because they are not sure when they will get the parts.
If rust gets deep for being idle for long time and my brake goes bad few months after I get my car, how can I make then liable?
Do I need to get some agreement with them for maintenance for one year after I get my car?

It is your vehicle. Bring it home or drive it.
What is the recall for? For most recalls the company sends you a letter telling you there is a recall, then another one telling you that the parts are available and to make an appointment. For my Jeep one recall took over seven months before they had parts, the latest was close to six months. I just keep driving it. Your car is six years old. I would go get it and drive it until they tell you they have the parts.

They will not cover rusting or brakes or anything like that, they are liable for something like it being hit by them or a contractor. Unless they had you sign a waiver when you left it there, even a verbal one.

Personally I would drive it. Sitting kills cars. When they have the parts, take it in. If the recall said something like "bring it in now" or else you would have a better position, but most are written to keep the owner in the dark.

After a month I would not leave it there, especially after I looked up the recalls It looks like you may be waiting a while.

The latest August recall #16V594000

Summary

Mazda North American Operations (Mazda) is recalling certain model year 2009-2010 Mazda6 vehicles manufactured February 4, 2008, to December 3, 2009. The protective coating may not have been properly applied to the air bag control unit (ACU) and, as a result, moisture may damage the unit causing it to malfunction.

Remedy

Mazda dealers will replace the ACU, free of charge, however parts are not currently available. The recall has begun but parts are not yet available. Mazda will mail a second notice when remedy parts are available. Owners may contact Mazda customer service at 1-800-222-5500. Mazda's number for this recall is 9816H.


The earlier recall #16V356000

Remedy

Mazda will notify owners, and dealers will replace the passenger frontal air bag inflator, free of charge. The recall began July 2016. Owners may contact Mazda customer service at 1-800-222-5500. Mazda's number for this recall is 9516E.

Both say the same thing though. They do not tell you to stop driving the car. Just that they know there is a problem and that they will fix it.
Now if you got the letter telling you that they have the parts and it will take X hours to replace it. I would verify that the dealer is doing the correct recall, they do not normally send out a letter like that unless the dealer has parts. It may be that the dealer thinks your car is in for the latest recall when it is actually the earlier one.
Either way I would check closer.

The question that needs to be asked is the car safe to drive, will airbag deploy when needed or any time it feels like it? Can airbag be disconnected? Should it be disconnected? Is there a liability issue?

The recall is for airbag. When I went for the service they said the parts were available for service.
After they removed by airbag they realised that they didn't have exact airbag for my car.
So now my car is sitting idle in open space at the dealer with airbag removed.
I don't think its safe to drive.
I asked them could they install another airbag, they said it will be a liability issue.
I don't know what can I do.
I am sure it will take another few months to get it fixed.
I am worried about my car getting rusted

Call the 800 number for Mazdas customer service, explain to them that you took the car in for the recall, dealer didn't have the correct part, that they removed your old one and now you are worried about the car just setting there. They will usually try to help.