An underplay that is
- deliberate, and
- intended to help win the game by removing one's own bad aji, or in some other way simplifying the position.
but see also 
For example, in a competition game in a situation of time pressure, one may play in a way that probably loses points but seems on the basis of positional judgement still to leave one clearly ahead.
Such plays are always deprecated, from a coaching point of view. There is no way that underplays are safe, as a habit. It may be that one cannot read everything; but getting into positions that are well beyond what one can read is deprecated, too. For example, a safety play may be used definitely to prevent an invasion of one's territory. The need for one might have been caused by an earlier mistake, such as trying to take a big corner that is really too big, and will always be subject to bad aji.
On the other hand choosing a variation that simplifies into a clearly won endgame position, over another one that is complex but might lead to a larger win, cannot always be called a safety play. For example an exchange that brings the middle game to an end may theoretically lose points: but really there is no obligation on players to try to win by the largest possible margin in positions that are genuinely too complex to read out or count. There may be many ways to end a ko fight: you aren't always required to choose one that allows your opponent to fight on effectively.
Therefore there is perhaps a psychological element here: not all inartistic practical plays based on trying to win the game with low risk are safety plays that should carry a stigma. Maybe there could be a point that amateurishness has to be involved, too: the low-grade safety play falls short of being honte.
James Davies calls a "Safety Play" something entirely different. In his usage, a safety play is a tesuji that eliminates all possibility of resistance, where lesser moves either lead to ko or fail outright. An example from Tesuji (from the chapter "When Liberties Count":
is the "safety play". Now white wins without ko. In contrast, if white plays at a instead, then after black throws in at 1, white has to win an approach ko.