Both hydrophobic and hydrophilic residues can be buried, but it's considered most important to bury as many hydrophobic residues as possible. (The Foldit proverb is "blue outside, orange inside", referring to the blue and orange coloring used for hydrophilics and hydrophobics in default view options.)
When a residue is buried, it's not accessible to the solvent inside a cell. The solvent consists mainly of water.
Most of the proteins used in Foldit puzzles are found inside a cell. For other proteins, such as those found in the cell membrane, the solvent may be oily. For proteins of this type, the normal rules are reversed, so hydrophobic residues should be exposed, and hydrophilic residues should be buried.
Foldit puzzles rarely involve membrane proteins or other types of extracellular proteins. One such protein was found in puzzle 1344. Solutions to puzzle 1344 tended to score poorly due to the large number of hydrophobic residues.
The scoring method was adjusted, and puzzle 1344 was reissued as puzzle 1347.
In this rare case, the proverb for players changes to "orange outside, blue inside". Without modified scoring, there is no way to fold this type of semi-membrane protein effectively, and results are likely to be different than the "native" state of the protein.