I have found a few older discussions for this, but the answers are not precise enough. This is for a '99 Toyota Corolla CE.
I need to know the exact title of the under engine splash cover/shield/guard/shroud and debris shield that is a cover underneath the car that fits from the front of the car, the driver’s side, all the way to the passenger side. On car sites all I can find references to are partial covers for either the passenger or the driver’s side, or mud flaps. A mechanic also called it an “air dam” but when I look up parts with this name, it’s a completely different thing. So, if I’m to search websites for this part, what is the proper name?
On my Chrysler I believe it’s called a “belly pan”.
Splash guard. I rarely replace them.
Your best bet would to be take your car to a certified Toyota collision repair shop ( they used to be called body shops ). They should be able to tell you if one is even available or if it is just cosmetic and you can do without it.
It’s called the under engine shroud.
What this does is, it allows the air to flow smoothly under the engine at speed to reduce drag which increases fuel mileage.
Tester
unless you are using this 15 year old car for road trips I would just leave it off. It is just there to improve highway fuel economy and you would have to do a lot of highway driving to pay for it.
If you really want one, look in the junkyards.
See if you can find it in this link. Post back.
http://www.toyotapartsoverstock.com/default.aspx
Thanks for the link, however, I’ve not been able to find the part on toyotapartsoverstock for the '99 Corolla CE.
I’ve had it off for years, but have had to replace the surpentine belt numerous times, partly because the pulley mechanism was worn down, which I also replaced, but last week I heard more noise coming from the belt which means either part of the belt was scraped (again) or debris flew in… The belt looks fine now, so I think it was debris, although the pulley squeal is back again. So I’d like to replace the “shroud” or guard (or whatever you call it) if I can, to keep out debris, and help the air flow (which others have recommended). I don’t want to go to a body repair shop or dealership due to their overcharging. I already have a mechanic who will replace it if I can find the part.
I would put it back if you can–it’s there to keep mud/crud/water from getting on everything. In the old days it didn’t matter so much if the bottom of an engine got wet and cruddy–the worst that could happen was a slipping belt and a little more corrosion possibly. But modern cars have multiple sensors and wiring down there that will not last as long if constantly bombarded.
If it is missing water and debris can get up in the engine bay and mess up the belts and short out the alternator if it is low in the bay. Several Hondas on the forum died in the rain because they were missing the shield and the alternator got wet…
I think you are looking for the Engine under cover(s).
In this link look under body/radiator support/splash shields.
I have searched all the sites, but all I could find is the guard/cover for years '88-'92 and 2009-2013. Does this mean I have to convert my '99 Toyota Corolla into a 1992 or 2009 model just to get this part? A mechanic told me this part (for my exact year/model) is only available from the Toyota dealer at a high price. 
You can get any part you want online at a discount. Www.toyotapartsoverstock.com Do an image search on google and post the pic here of the part and we can help you find it in the parts catalog.
These shields are $37 each from a Toyota dealer online. If you want them for less you can look for used parts.