Snakum,
Yes, there are some airlines that offer sponsorships or "apprentice"-type training programs to low-hours pilots such as TR's friend. As far as I know (I could be wrong), there are no USA-based airlines who do this.
Thrust Reverser
I won't be at the American Airlines schoolhouse until later this week (Thursday). In the meantime, I've done some research that I hope is helpful to your friend. I am not an expert in any way, but here is what I have found so far:
Out of all of the major airlines who list total-time hours requirements on their websites, the minimum total time listed is 1000 hours. However, most listed 1200-1500 hours TT as a minimum. There were also additional sub-requirements listed such as turbine or multi-engine time (anywhere from 300-1000 minimum hours listed), PIC time (300-700 hours), and instrument time. All require a commercial certificate with an instrument rating as well. Even on the commuter airline side, many companies require in the neighborhood of 1000 hours TT. There are some exceptions, especially if the candidate has acquired an aviation degree or has completed other "formal" types of training such as a military flight school or civilian flight academy program. One commuter airline categorizes "0 to 1200 hour pilots" as "pilots with little to no experience" and the only thing they offer you is the opportunity to apply to their academy (and you pay the training costs).
As an aside, I personally detest gloom-and-doom or "naysayer" mindsets, so I do wish your friend all the best in her future flying career. Hopefully she won't be deterred from flying by the above facts, but will instead see the reality of her need for more flying experience. I commend her initiative in preparing for the ATP written exam. However, that exam is only one small step in the entire process, and more hours/experience is what is really needed. Applying to a major US airline with 300 hours is akin to applying for a PHD program with only a high-school education. The analogy may be a bit exaggerated, but you get the point that some very important steps are being skipped. The bottom line is that she needs to fly more: work toward increased ratings, certificates, and overall experience; consider becoming an instructor; consider hours-building in countries where the flying costs are relatively low. If she keeps working at it, she should attain her goals eventually.
Feel free to e-mail me (or have her e-mail me) directly if more info is needed. I'll post another reply after I get the info from AA.