Quiescent Nodes are nodes at depth zero or below, where a Quiescence Search is performed  . The most top subset of quiescent nodes at depth zero are also called horizon nodes. If the quiescent node is an expected Cut-Node, that is the evaluated standing pat score is already greater or equal than beta, the quiescent node becomes a leaf with the lower bound score of beta (fail-hard) or the stand pat score (fail-soft). Otherwise, winning captures (or checks) may either cause a beta-cutoff or raise alpha with an exact score at PV-Nodes. At expected All-Nodes with evaluated score (far) below alpha, if no tactical move is available, or due to Delta Pruning good enough to raise alpha, those leaves return alpha (fail-hard) as an upper bound. This may also appear, if this quiescent node was not a leaf, since some captures were not pruned, but tried without raising alpha.
- quiescent nodes, and history heuristic... by Joel Veness, CCC, January 30, 2003 » History Heuristic
- Quiescence node explosion by sandermvdb, OpenChess Forum, June 01, 2016