In ice-hockey, will goalie be credited with a shutout if he was the only goalie in that game and has a 100% save percentage but was pulled out on a delayed penalty (or simply near the end of the game) and the opposing team scored an empty net goal?
I don't see a reference explicitly for this in the NHL rules; the NCAA rules do mention shutouts, but don't actually define them - here, for example:
Article 3. If two or more goaltenders from the same team participate in a shutout, credit the team with a shutout but do not award any goaltender an individual shutout. A goaltender must be solely responsible for holding the opposition scoreless to be credited with a shutout.
Note: Empty-net time (i.e., during a delayed-penalty call) does not preclude a goaltender from being awarded a shutout.
That refers to whether a goaltender can get sole credit for the shutout, but isn't talking about goals scored during the shutout.
I would suggest, though, that it is required to have a shutout for the team before a goaltender can get credit. It may simply be rare enough of a possibility to even consider (no team would go empty net with 0 goals given up, and goals are so rarely scored on delayed penalties by the offending side (as it requires one of the offended players to accidentally score on their own goal) that it simply doesn't come up).
There is at least one case of this happening. In 2016, the Canucks season opener was a 2-1 victory in OT, and the -1 was an own goal by Loui Eriksson.
See this box score; Ryan Miller has 64:57 TOI, no goals allowed, and 0 shutouts.
Although goalies are awarded shutouts when their team wins without conceding a goal, it really is a team event that also counts towards an individual's stats.
For example, imagine a goalie getting injured and so pulled from the match half way through. If both the started and the back up don't let in a goal, the team wins without conceding a goal and records a shutout. But neither goalie is awarded shutout. An example of a team shutout, but not an individual shutout, is Islanders vs Penguins, 2011-02-02, where 2 goalies were used by the Penguins after Brent Johnson was ejected.
Similarly if there is a goal allowed while no goalie in the net, neither the team or the goalie is awarded the shutout.