Bit of a disclaimer first - Since this is a matter of money, you should reach out to the Red Hat support personnel for an authoritative answer. They will be able to provide the information specific to your deployment of Red Hat Enterprise Linux. I have added my references in this answer, but please take the steps to verify it yourself.
There are two aspects you are considering here: one is the subscription, and the other is the life cycle.
The subscription part is fairly straightforward. Starting from RHEL 4, you need an active subscription to run RHEL at all stages of the RHEL life cycle. The Red Hat Enterprise Linux Life Cycle page defines the life cycle as follows:
Red Hat offers subscription services for each major release of Red Hat
Enterprise Linux throughout four life-cycle phases—called Full
Support, Maintenance Support 1, Maintenance Support 2, and an Extended
Life Phase.
The same document goes on to say:
Software changes to Red Hat Enterprise Linux are delivered via
individual updates known as errata advisories through the Red Hat
Customer Portal or other authorized portals.
....
All released errata advisories remain accessible to active subscribers
for the entire Red Hat Enterprise Linux life cycle.
This document on the Extended Life Cycle Support Add-On is more specific on the subscription requirement during the Extended Life Cycle Phase:
What is the difference between the Extended Life Cycle Phase and the
Extended Life Cycle Support Add-On?
The Extended Life Cycle Phase (ELP) is the post-retirement time
period. We require that customers running Red Hat Enterprise Linux
products beyond their retirement continue to have active subscriptions
which ensures that they continue receiving access to all previously
released content, documentation, and Kbase articles as well as receive
limited technical support.
There is another document here the states the same: Do retired (EOL) RHEL products still need a subscription?
That should answer the first part of your question. You need to have an active subscription as long as you are running RHEL 6, and you will continue to have access to the package repositories on RHN as long as your subscription is active.
The second aspect, the stage of the life cycle, determines what you are actually able to get from Red Hat as part of your subscription. This is summarized as a table on Life Cycle page, but the key information is as follows.
During the Extended Life Phase, there will be no more work done on that specific version of RHEL. There will be no more bug fixes, security fixes, software enhancements or minor releases. Technical support will also be limited, and is restricted to existing installations. Basically, that major version of RHEL will be frozen in time. You will still have access to all the fixes delivered previously, but nothing new will be delivered during ELP.
To quote to the Life Cycle document once again:
During the Extended Life Phase, a Red Hat Enterprise Linux
subscription provides continued access to previously released content
on the Red Hat Customer Portal, as well as other content such as
documentation and the Red Hat Knowledgebase. Advice for migrating to
currently supported Red Hat Enterprise Linux versions may also be
provided.
For versions of products in the Extended Life Phase, Red Hat will
provide limited ongoing technical support. No bug fixes, security
fixes, hardware enablement or root-cause analysis will be available
during this phase, and support will be provided on existing
installations only.
For customers who are unable to migrate from a version of RHEL in the Extended Life Phase, Red Hat also provides the Extended Life Cycle Support Add-On. This is an additional subscription that will allow you to receive critical security & bug fixes during the Extended Life Cycle Phase. You can refer to this document for details on the ELS offering: What is the Red Hat Enterprise Linux Extended Life Cycle Support Add-On (ELS), and what is its support life cycle?
Purchasing the ELS Add-On gets you access to a new repository which delivers the ELS-specific fixes. There are also restrictions on what is supported with the ELS Add-On, so I suggest you read though the document carefully.
I was also able to find this FAQ on the retirement of RHEL 5: FAQ: Red Hat Enterprise Linux 5 Reaches End of Full/Maintenance Phases and Transitions to Extended Life Phase. As the date of retirement of RHEL 6 approaches, you can expect a similar document to be released for RHEL 6 as well. I will try and update this answer when that happens.