If you block a contact then that is exactly what happens. The contact gets blocked and the contact's texts will not be delivered. I am not sure what is the point of blocking someone and yet still receive the texts. If your goal is to receive texts from a contact without any notification sound, then you can mute the contact instead of blocking it.
To mute a contact, open the Messages app and locate the text conversation with this contact from the list of conversations. TOUCH the conversation and SWIPE LEFT. Tap on the Bell icon. This will mute that contact and conversation. You will not be notified that there is a text from from that contact, however, you will receive their texts.
Axel F.