Shown here is False Solomon's-seal, Smilacina racemosa. This fellow has delicate alternate-leafed plants that do well in in partial-shade to shady areas, but tend to flop over if not using a tree for support. It develops pyramidal clusters of small white blooms in late May-early June that a month or so later turn into little round red berries a little smaller than BBs. This is a slow grower but hardy; my wife planted a specimen about 20 years ago in a difficult shady area and it returned every spring for about a decade; in recent years I've found other speciments on the property and grouped them, and now it seems to be multiplying.
False solomon's seal is easily confused with its namesake, Solomon's-seal, or Polygonatum biflorum. You can tell the "false" one by its flowers (above) and seeds (below).
This perennial does not spread much, but is considered disease-resistant and rugged.