Sometimes a person can read texts online. The ability to read text messages online depends on the phone carrier and the services that are provided.
Many cellular service providers offer access to online text messaging that can be read on the receiver's phone. When the receiver replies, it comes up on the sender's phone just like a normal text message. There is usually not a fee for this service. AT&T and Verizon are two of the leading cell phone providers that offer online texting.
If a person wants to find out if their carrier offers the service, they can ask them directly when they sign up or they can go online and check the provider's website. It is important to be careful that there aren't any extra fees for using the service. If it is offered, there will be precise instructions on how to use it, and an explanation of any fees.