More information is needed. Where do you live? (What is the climate like?) What do you mean by "encapsulation".

Fungus grows where there is food (wood), moisture (ground), and a lack of light and ventilation. If you seal the space you will have to stop the moisture from rising up from the ground or you will have to mechanically dehumidify the space, or possibly both.

More info:
Missouri/Arkansas border- Table Rock Lake. 90s & humid in the summer..December temps are teens to 20 , but only 43 in my closed up crawlspace.

Open crawlspaces in hot humid climates might have been a good idea before air conditioning, but with the addition of AC, you can get condensation because the temp of the floor is below the dew point. Where I live, on the Gulf Coast, sealing the crawl space is recommended. Your only alternative is to spray foam insulate the floor. There are two places that you might start to gather information to help you decide. Try your agricultural school and http://www.buildingscience.com/index_html

You can try sealing seams in the plastic, and then sealing to tot eh foundation.

Fastening to the foundation usually the harder part.

I have used various 'plastic' boards (including ones designed for decks) fastened to the inside of the foundation with siliconized latex caulk behind the boards to seal there.

The plastic is then sealed to the face of the board.
If you use deck width boards you can usually rip them at least in half, and sometimes narrower if you then treat them gently.