Class A power amplifier, how to calculate base voltage after removing collector load
When \$R_L\$ is connected, \$R_{E1}\$ and \$R_{E2}\$ are fed predominantly by the collector current.  The base provides only a small fraction \$1/(\beta+1)\$ of that current.  In this case, the base voltage is primarily determined by \$R_1\$ and \$R_2\$.

When you disconnect \$R_L\$, there is no source for current to \$R_{E1}\$ and \$R_{E2}\$ except from the base.  This draws significant current from the voltage divider on 15V comprised of \$R_1\$ and \$R_2\$.  This is represented by its Thevenin equivalent so that the network can be analyzed as a series circuit.  The transistor, with no collector connection, is essentially a diode.