brink

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun The upper edge of a steep or vertical slope: synonym: border.
• noun The margin of land bordering a body of water.
• noun The point at which something is likely to begin; the verge.

from The Century Dictionary.

• noun The edge, margin, or border of a steep place, as of a precipice or the bank of a river; verge; hence, close proximity: as, “the precipice's brink,”
• noun to be on the brink of ruin.
• noun Synonyms See rim.

from the GNU version of the Collaborative International Dictionary of English.

• noun The edge, margin, or border of a steep place, as of a precipice; a bank or edge, as of a river or pit; a verge; a border. Also Fig.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun The edge, margin, or border of a steep place, as of a precipice; a bank or edge, as of a river or pit; a verge; a border; as, the brink of a chasm. Also used figuratively.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• noun the edge of a steep place
• noun a region marking a boundary
• noun the limit beyond which something happens or changes