Unfortunately, that is not the case with any but a very few high end systems for banks and such. Residential alarms are typically monitored using the switched telephone network. In somple terms, the alarm makes a phone call to the central monitoring station's alarm receiver. If the line is cut no call is made and the alarm company does not know it.
Many years ago it was common to build systems with "line security." A dedicated copper pair was connected from the protected premises, through the telephone company central office to the alarm central station. A voltage was applied to the cable. Two different resistors were wired between the circuit and earth ground. Shorting one resistor meant burglary or holdup. Shorting the other meant fire. A line cut showed as a trouble condition.
In another ancient system a loop of cable was connected from the alarm company, through the C.O. and then through an alarm Mc Cullough (I forget how it was spelled) transmitter at each protected premises. Upon alarm a motorized cam wheel would close and open a switch, creating a series of interruptions in current on the loop. At the alarm company office this was translated into a series of marks or holes in a tape designating the account number. A clerk then looked up the account called the local authorities. If the line was cut an alarm company agent would be dispatched to investigate. The problem is these loops were long and many properties were often connected to each loop. It could take many hours just to find which property has a fault.
Another problem with leased line security is most telco's don't want to provide the dedicated copper pairs any more. They can make far more profitable use of that single pair as part of the dial-up system. Finally, new outside plant lines are gradually switching over to fiber optic which does not support inexpensive line security devices.
No offense, but the primary purpose of this newsgroup is to provide a place where people can share information on alarms. The gentleman's query is on-topic and appropriate.