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The brake system is hydraulic with the reservoir higher than the calipers so all fluid will drain out, it will not "gush out" but will "ooze" out. Place an oil pan or similar under each wheel as you do the work to collect the fluid. Do not bother pouring more fluid into the reservoir until after you are finished and have everything bolted up tight. Then perform a bleed on the system to remove the air.
I think he meant, do not let the resevoir get empty while bleeding the brakes. The mess happens when you start to bleed the system. When you disconnect the line you will have a very small amount of leakage. When I did mine I filled the resevoir after I finished each wheel and that worked fine for me.
You really will not lose that much fluid on each wheel. 1-2 0Zs at most. Have all the replacement parts sitting there ready to go as you take the old lines off. Time is your friend in terms of a quick re- installation and minimizing loss of fluid. Remove line and washer from caliper then from the steel line on car. A drip pan is a good idea. Do not do job without proper line wrenches - you will be really pissed if you strip a fitting !!! Check the master cylinder resevoir fluid level after each line change. DO NOT let it run dry or you have complicated your change out by having to bleed the master. Bleed in standard fashion after final change out and you will be fine. Not difficult - should not take more than 2 hours start to finish for a first timer.