Negative rights are those you have purely by virtue of being alive, eg right to life, freedom of association, etc. It also includes things like the right to work, food, etc however it doesn’t require that someone else gives you a job or food. You may have to provide those for yourself.
But for me to exercise those rights (working, eating, etc.), I (may) need (police) protection from outside forces (criminals) attempting to interfere with my exercising those rights.
I still fail to discern the difference between so-called "positive" and "negative" rights. In both cases, I have to be able to invoke the assistance of the State in order to exercise them.
Perhaps using different terminology would help: Let us speak instead of "rights" (to go on a 6-week vacation in the tropics - provided we can AFFORD to pay for it ourselves; to express our opinions - provided we can AFFORD to take out a full-page ad in the paper; to a 4-year education at Harvard - provided that we AFFORD to pay the tuition and provided that we meet Harvard's admission requirements*) - all of which are predicated upon availing ourselves of police protection in the event that some third-party attempts to interfere with our exercise of our rights - and "entitlements" (to govt. largesse). (And yes: I am aware that the term "entitlement" has hitherto referred to rights that are earned - e.g., S.S.)
*Determining the Constitutionality of those admission requirements (which might include, e.g., racial quotas) is another matter, and deserves a separate discussion.
Regards,