An emergency loan is a short-term signing made outside a transfer window to cover an unexpected shortage, most often an injured goalkeeper. FIFA rules restrict registrations outside windows, so where they survive they are narrow exceptions granted by a league rather than a general route into the market.
English football once ran a broad version of this. Clubs in the Football League could borrow players outside the window on short deals, and lower-division squads were built around the availability of them, until FIFA's insistence that registrations happen inside windows forced the system to be withdrawn.
What remains tends to be goalkeeper-specific and tightly conditioned. A club that loses its senior goalkeepers to injury or suspension has a problem no outfield substitution solves, so competitions have generally kept some route to registering cover in that one position.
The wider point is that the window is a registration rule, not a contract rule. A club can agree whatever it likes at any time of year; what it cannot do outside a window is make a new player eligible to play, and exceptions to that are granted narrowly.