Will non-smart phones install software that steals text messages and calls?

Of course. But the situation with smartphones is different.

However, these softwares have been installed before being handed over to users, instead of being installed and uninstalled at any time like smart phones now.

For example, some of Motorola's mobile phones are prohibited from being used in important security departments and the military because they may be remotely controlled and eavesdropped. These mobile phones have been specially modified and installed with special software before being handed over to users, which can be eavesdropped, sent by SMS or email, or directly controlled remotely.

There are also some specially modified shanzhai machines that also have eavesdropping function.

Before the emergence of smart phones, before entering secret meetings or key departments and parts, mobile phones should be placed in a secret cabinet with electromagnetic shielding function. What's more, it is to prevent being eavesdropped.