In this sort of situation there are two possible problems.
1. A labour ban.
2. Getting a new employment entry permit (employment visa) issued. This is not the same as a work permit (labour card) or residence visa.
1. As long as a residence visa and work permit application has not been started, you can take up another job offer without any labor ban being imposed. Once the residence visa process has started, then you are employed, and if you quit, an automatic 6 month labour ban will usually apply, possibly 1 year if you have worked for less than one year or broken a fixed term contract.
That doesn't really apply in your case, but I'm adding that for other readers of this topic who might be in that situation.
2. As long as a valid employment entry permit is in the UAE immigration system (or any sort of entry visa), any new visa application under the same name will automatically be rejected.
Normally an entry permit is valid for 2 months or 60 days before it must be used, if it is not used during that time it automatically expires, and you can then apply for a new entry permit or visa.
If a company has applied for an employment visa and it has been issued, but you don't want to use it, you cannot cancel it yourself. However, the company can apply to the immigration department to get it cancelled.
If the company has not applied for an employment visa yet, then your new employer should be able to apply for one and get your name in the system before your previous employer does. In which case, their application will be blocked.
I don't think any of the above is different for free zone companies versus mainland companies.
I'm not familiar with the term "pre work permit approval from the MOL" with respect to the UAE visa and work permit process.
You could contact your first employer and say due to a sudden change in personal circumstances you are unable to take up their job offer and could they please not go ahead with the visa application, or cancel it if they have. Don't tell them you have another job offer.
Before or after (perhaps before), suggest to your second employer that they file an application for your employment entry permit as quickly as possible. You'll soon find out if it's possible or not.
You could also contact the MOL and DNRD to see what entry permit, if any, is in their system under your name.http://www.dubaifaqs.com/dnrd.phphttp://www.dubaifaqs.com/jobs-in-dubai.phphttp://www.dubaifaqs.com/ministry-of-labour-uae.php