It's not typical in the US for employers to "need" prior salary information (much less proof in the form of W2s or paystubs) in order to make an employment offer. In fact, it's illegal in some states for employers to request your prior salary, and as a result, many employers who used to ask have stopped, even if their state doesn't (yet) have a ban.
The process of negotiating salary is like any other negotiation - both parties are trying to optimize their own set of criteria. Typically, the employer is trying to pay as little as possible for a given skill set (although some employers will interpret this differently, some will see the value in paying more for people they really want while others are just looking to pay the least to the cheapest person).
Employers know that potential candidates are likely to compare any salary offer with the current (or most recent) salary. People looking for a new job don't like to feel like they're making LESS at the new job than at the old one. Therefore, if the employer can determine (and prove) what you were making in your last job, they know a theoretical "floor" of what you'll accept: If they know you were making $50k, and they had budgeted $80k, they may only offer you $55k instead of the full $80k, and tally a $25k annual savings as a result. Meanwhile, if they didn't know you were making $50k, and you pushed for $70k, they'd probably happily offer you $70k.
In other words, they use the knowledge of your prior salary as leverage against you in the negotiation.
So, what do you do when asked for this information?
- Determine if it's legal for the employer to ask in your state. If not, you can let them know this.
- Redirect them to your desired salary: "My last salary was based on the job I was performing for my last employer. What I'm interested in talking about is the job I'm going to be performing for you, and I think that is worth $X." If the request comes in the form of a spot on an application, leave it blank and indicate something along the above sentence in any comments or notes on the application.
- If asked for paystubs, or confirmation of your salary via some other documentation, inform them that you're not comfortable sharing documentation that contains personal information, and that information about your salary at your last employer is proprietary to that company.
It can be hard, as a job candidate, to essentially say no to something a potential employer is asking for, but if they push hard for you to give them information you're not comfortable sharing, you have to ask yourself: Do you actually want to work for a company that is essentially playing dirty right from the start, when trying to negotiate your salary? There are always other jobs out there...