I would imagine you have somewhere near the top of your body section (perhaps existing as a snippet or embed) a bit of if/then code that would be along the lines of
<div id="login">{if logged_in}<span class="user">Hello, {username}!</span> [<a href="http://{path=community/profile}" rel="nofollow">My Account</a>] [<a href="http://{path=logout}" rel="nofollow">Log Out</a>]{/if}
{if logged_out}<span class="user">Hello, Guest!</span> [<a href="http://{path=community/login}" rel="nofollow">Login</a>] [<a href="http://{path=community/register}" rel="nofollow">Register</a>]{/if}</div>
(I’ve changed the “members” path to “community”, as you can see above, in Members/Preferences/Profile Triggering Word - you likely should do similarly as the default “members” is abused and triggers some issues nowadays.)
If so, look for either code explicitly describing the breadcrumb generation, or either an embed or a snippet which has this code.
Once you find that, include it in both the if logged_in AND the if logged_out portions.
That should do it! Let me know how you fare.