How do I convert an inexact number smaller than $MinMachineNumber to machine-precision?

This situation is comparable to

$MinMachineNumber / 2

automatically giving an arbitrary precision result.

Precision[$MinMachineNumber/2]
(* 15.9546 *)

Mathematica detects the underflow condition and switches to arbitrary precision arithmetic. This can be turned off:

SetSystemOptions["CatchMachineUnderflow" -> False]

Now the result of $MinMachineNumber/2 has MachinePrecision. The result is not 0., but a denormal number, I believe (my knowledge is lacking in this area). If you divide by a number larger than 10^$MachinePrecision then you get a 0..

$MinMachineNumber/2
(* 1.11254*10^-308 *)

$MinMachineNumber/10^15
(* 2.5*10^-323 *)

$MinMachineNumber/10^16
(* 0. *)

SetPrecision works as you want it, too.

number = 5.803736411761291186334053015446685`16*^-400;
number1 = SetPrecision[number, MachinePrecision]
(* 0. *)

SetPrecision will not create denormal numbers, it seems.

SetPrecision[1.2`16*^-308, MachinePrecision]
(* 0. *)

number = 5.803736411761291186334053015446685`16*^-400;
number + 0.
(* 0. *)

N makes arbitrary precision numbers when either given a second argument or a number not representable by a machine number as its first argument. However, machine numbers in expressions generally coerce arithmetic into the machine domain.

Another way:

toMPReal = Compile[x, x][#] &(*/.c_Compile :> RuleCondition[c]*);

toMPReal[5.803736411761291186334053015446685`16*^-400]
(*  0.  *)

Uncomment the replacement rule to pre-compile the function.