Web servers will typically remove multiple slashes before the application gets to see the request,for a mix of compatibility and security reasons. When serving plain files, it is usual to allow any number of slashes between path segments to behave as one slash.
Blank URL path segments are not invalid in URLs but they are typically avoided because relative URLs with blank segments may parse unexpectedly. For example in /module/search, a link to //subject/param is not relative to the file, but a link to the server subject with path /param.
Whether you can see the multiple-slash sequences from the original URL depends on your server and application framework. In CGI, for example (and other gateway standards based on it), the PATH_INFO variable that is typically used to implement routing will usually omit multiple slashes. But on Apache there is a non-standard environment variable REQUEST_URI which gives the original form of the request without having elided slashes or done any %-unescaping like PATH_INFO does. So if you want to allow empty path segments, you can, but it'll cut down on your deployment options.
There are other strings than the empty string that don't make good path segments either. Using an encoded / (%2F), \ (%5C) or null byte (%00) is blocked by default by many servers. So you can't put any old string in a segment; it'll have to be processed to remove some characters (often ‘slug’-ified to remove all but letters and numbers). Whilst you are doing this you may as well replace the empty string with _.