Modern UPS products are designed to cope with overloads.
An overload can take one of several forms and current electronic solutions to limit system damage are based on simple principles.
The UPS is being overloaded if the load power demand is greater than the rating of the UPS.
An overload may happen quickly, or slowly increase above the rating of the UPS. Inside the UPS there are current switching devices which can cope with minor overloads for a considerable time until they become too hot. These switches will be damaged almost instantaneously by currents way in excess of their rating.
It is commonplace to find overloads of 125% or 150% of rating being allowed by the electronics for some seconds or even minutes. However larger overloads for example 10x rating require faster action by the electronics.
Most users do not realise that some modern electronic power supplies take large currents when first powered up. It is not unusual for a small computer such as a PC controlling a process plant to be on 24/7. The operator may well choose to switch off the monitor during the night when no-one is looking at it - either to save power or increase monitor life.
In the morning when the operator returns and switches on the monitor which normally consumes only about 50 watts the switch on surge has a power equivalent of maybe 10000 watts albeit only for one thousandth of a second.
This load would typically destroy the UPS and the normal solution is to detect the overload and divert it around the UPS. This is achieved entirely automatically by a small switch which quickly connects the load directly back to the mains until the overload disappears. This switch is called a 'bypass'.
So far so good. The UPS happily protects itself and each morning when the monitor is switched on momentarily switches the load back to mains and reverts to the battery supply a very short time later.
During a power outage this option becomes unavailable. The UPS must NOT be overloaded during battery operation when the mains is not present. If an overload occurs the UPS will protect itself and sadly drop the critical load because it has no power source for the overload.
This problem can really only be managed by knowledge and discipline unless further investment is made (which is usually quite substantial) to overcome it.