Internal architecture of cursors
Depends on the cursor type, as documented in Concepts: Cursors:


  Forward-only
  
  A forward-only cursor does not support scrolling; it
  supports only fetching the rows serially from the start to the end of
  the cursor. The rows are not retrieved from the database until they
  are fetched ... Although the database API cursor models consider a
  forward-only cursor to be a distinct type of cursor, SQL Server does
  not. SQL Server considers both forward-only and scroll as options that
  can be applied to static, keyset-driven, and dynamic cursors.
  
  Static 
  
  The complete result set of a static cursor is built in tempdb when the
  cursor is opened. ...
  
  Keyset
  
  The membership and order of rows in a
  keyset-driven cursor are fixed when the cursor is opened.
  Keyset-driven cursors are controlled by a set of unique identifiers,
  keys, known as the keyset. The keys are built from a set of columns
  that uniquely identify the rows in the result set. The keyset is the
  set of the key values from all the rows that qualified for the SELECT
  statement at the time the cursor was opened. The keyset for a
  keyset-driven cursor is built in tempdb when the cursor is opened.
  
  Dynamic
  
  Dynamic cursors are the opposite of static cursors. Dynamic
  cursors reflect all changes made to the rows in their result set when
  scrolling through the cursor. The data values, order, and membership
  of the rows in the result set can change on each fetch. ...


As for memory use, all data access goes through the buffer pool, see Memory Manager Architecture. There is no 'close' nor 'deallocation' occurring. Data is brought in memory as needed, it may be referenced by multiple queries, and evicted only when more free memory is required.