Let "extending by $0"$ be an operation that takes a language and appends a $0$ to the end of every string in the language. For example, if $L=\{,01,010,1111\},$ then extending $L$ by $0$ would yield $\{0,010,0100,11110\}.$ Describe how to construct a DFA that could be used to prove that regular languages are closed under extending by $0.$

You do not have to prove that your DFA accepts then "extension by $0"$ language, but your solution should be still valid for infinite languages.